Problems on Rate of Interest

Rate of Interest

Q.1.  The simple interest accrued on an amount at the end of five years at the rate of 12.5. p.c.p.a is Rs. 1575. What is the amount?

(a) Rs.2050    (b) Rs.2550   (c) Rs.2250      (d) Rs.2520    (e) None of these

Ans: (d) Rs. 2520

Explanation:

Principal (here, the amount) = Simple Interest × 100/ Rate × Time

                                              = 1575 × 100/5 × 12.5 = Rs.2520. Ans.

Q. 2. Mahesh invests an amount of Rs.8560 @  4 p.c.p.a. for 2 years. What approximate amount of compound interest will he obtain at the end of 2 years?

(a) Rs.684    (b) Rs.689     (c) Rs.645    (d) Rs.698      (e) Rs.720

Ans: (d) Rs. 698

Explanation:

Compound interest = P ( 1 + r/100 )ⁿ  - P

                               = 8560 (1+ 4/100)² - 8560 = 8560 (100 + 4/100)²

                              = 8560 ( 104/100)² - 8560 = 8560 × 104/100 × 104/100 - 8560

                             = 8560 × 26/25 × 26/25 – 8560 = 9258 – 8560 = Rs.698. Ans.

Q.3. Anurima invests an amount of Rs.12710 on simple interest after a certain period. For how many years did she invest the amount to obtain the total sum?

(a) 6 years   (b) 8 years    (c) 5 years    (d) 4 years    (5) None of these

Ans: (a) 6 years.

Explanation:

Term ( or no. of years etc ) = Simple Interest × 100/Principal × rate

                                Simple Interest = Rs.12710 – Rs.10250 = Rs.2460

         Therefore, the term = 2460 × 100/4 × 10250 = 6 years. Ans.

Q. 4. What would be the simple interest obtained on an amount of Rs.4450 at the rate of 9 p.c.p.a. for 2 years?

(a) Rs.807    (b) Rs.811   (c) Rs.810    (d) Rs.801   (e) None of these

Ans: (d) Rs.801

Explanation:

Simple Interest = Principal × Rate × Term/100

                         = 4450 × 9 × 2/100 = Rs.801. Ans.

Quickest way:

Find the SI for 1 year mentally i.e. =Rs. 400.5       (SI is For Rs.100 per year)

For 2 years take its double i.e. = Rs.801.Ans.

Q. 5. Rashi deposits an amount of Rs.95000 at the rate of 12 p.c.p.a simple interest for 4 years. What total amount will Rashi get at the end of 4years?

(a) Rs.45600   (b) Rs.93100   (c) Rs.140600   (d) Rs.188100   (e) None of these

Ans: (c) Rs. 140600

Explanation:

Total Amount = Principal + Simple Interest

Simple Interest = Principal × Rate × Term/100

                         = 95000 × 12 × 4/100 = Rs.45600

Therefore, the amount = Rs.95000 + Rs.45600 = Rs.140600.Ans.

Q. 6. What compound interest will be obtained on an amount of Rs.2500 at the rate of 12 p.c.p.a. in 2 years?

(a) Rs.550    (b) Rs.608    (c) Rs.596   (d) Rs.636    (e) None of these

Ans: (d) Rs.636

Explanation:

Compound Interest = Principal ( 1+ r/100 )ⁿ - Principal

                                = 2500 (1 + 12/100)² - 2500

                               = 2500 × 112/100 × 112/100 – 2500

                               = 2500 × 56/50 × 56/50 – 2500 = Rs.3136 – Rs.2500 = Rs.636. Ans.

Q. 7. A man will get Rs.180 as simple interest on Rs.1200 at 5% per annum in

(a) 3 years    (b) 4 years     (c) 5 years        (d) 2 years    (e) None of these

Ans: (a) 3 years

Explanation:

Term = SI × 100/P r

         = 180 × 100/ 1200 × 5 = 3 years. Ans.

Q. 8. What would be the compound interest accrued on an amount of Rs.45400 at the end of two years at the ratio of 15 p.c.p.a.?

(a) Rs.16411.5    (b) Rs.14461.5     (c) Rs.16461.5    (d) Rs.14641.5   (e) None of these

Ans: (d) Rs.14641.5

Explanation:

Compound Interest = Principal (  1+ r/100)ⁿ – Principal

                                = 45400 ( 1 + 15/100)² - 45400

                               = 45400 × 115/100 × 115/100 – 45400

                              = 45400 × 23/20 × 23/20 – 45400

                             = 454 × 23 × 23/ 2 × 2 – 45400 = 60041.5 – 45400 = Rs.14641.5. Ans.

Q. 9. In what time will Rs.500 amount to Rs.650 at 6% per annum?

(a) 3 years    (b) 5 years   (c) 6 years     (d) 7.5 years    (e) 8 years

Ans: (b) 5 years

Explanation:

Term = SI × 100/ P r

SI = Rs.650 – Rs.500 = Rs.150

Term = 150 × 100/ 500 × 6 = 5 years. Ans.

Q. 10. An amount of Rs.45000 become Rs.77400 on simple interest in eight years. What is the rate of interest p.c.p.a.?

(a) 9    (b) 11    (c) 8      (d) 10.5      (e) None of these

Ans: (a) 9

Explanation:

Rate of interest = SI × 100/P n

SI = Rs. 77400 – 45000 = Rs. 32400

Therefore, Rate = 32400 × 100/ 45000 × 8  = 9% p.a. Ans.

Q. 11.  What amount of compound interest can be obtained on an amount of Rs.4800/- @ 6 p.c.p.a. at the end of 2 years?

(a) Rs.544.96    (b) Rs. 576/-    (c) Rs.593.28    (d) Rs.588/-    (e) None of these

Ans: (c) Rs.593.28

Explanation:

C I = P ( 1+ r/100 )ⁿ – P

      = 4800 ( 1 + 6/100 )² - 4800

       = 4800 × 106/100 × 106/100 – 4800

     = 4800 × 1.06 × 1.06 – 4800 = 5393.28 – 4800 = Rs.593.28. Ans.

Q. 12. What would be the simple interest obtained on an amount of Rs.6535 at the rate of 10 p.c.p.a. after 6 years?

(a) Rs.3414    (b) Rs.3921   (c) Rs. 3807    (d) Rs.3149     (e) none of these

Ans: (b) Rs. 3921

Explanation:

Simple Interest = PRN/100

                         = 6535 × 10 × 6/100 = Rs. 3921. Ans.

Q. 13. At what rate of simple interest per annum can an amount of Rs. 1553.40 be obtained on the principal amount of Rs.8630 after 3 years?

(a) 8 p.c.p.a     (b) 4 p.c.pa.    (c) 5 p.c.p.a.    (d) 7 p.c.p.a.   (e) None of these

Ans: (e) None of these

Explanation:

Rate = SI × 100/ P n

S I = Rs.1553.40; Principal = Rs.8630;   term = 3 years

Therefore, the rate of interest = 1553.40 × 100/8630 × 3 =  5178/863 = 6%. Ans.

Q. 14. Mr. Anuraag Awasthi deposits an amount of Rs.56500 to obtain a simple interest at the rate of 12 p.c.p.a. for 3 years. What total amount will Mr.Anuraag Awasthi get at the end of 3 years?

(a) Rs.75680     (b) Rs.77540   (c) Rs. 76840     (d) Rs.73420      (e) None of these

Ans: (c) Rs.76840

Explanation:

SI = Principal × Rate × Term/100

Therefore, Simple Interest = 56500 × 12 × 3/100 = Rs.20340

So, the Total Amount = Rs.56500 + Rs.20340 = Rs.76840. Ans.

Q. 15. What would be the compound interest obtained on an amount of Rs.7800 at the rate of 5 p.c.p.a. after 3 years?

(a) Rs.1235.685      (b) Rs.1229.475      (c) Rs.1287.680   (d) Rs.1248.750   (e) None of these

Ans: (b) Rs.1229.475

Explanation:

C I = P (1 + r/100 )ⁿ –P

      = 7800 ( 1 + 5/100 )³ - P

      = 7800 × 105/100 × 105/100 × 105/100 – 7800

      = 7800 × 21/20 × 21/20 × 21/20 – 7800 = Rs.9029.475 – Rs.7800 = Rs.1229.475, Ans.

Q. 16. Sonia invested an amount of Rs.17500 at the rate of 8  p.c.p.a. After how many years will she obtain a simple interest of Rs.16800?

(a) 15 years    (b) 8 years  (c) 9 years    (d) 12 years    (e) None of these

Ans: (d) 12 years

Explanation:

Term = SI × 100/P r

         = 16800 × 100/17500 ×8

         = 12 years. Ans.

Q. 17. If Rs.600 becomes Rs.3600 in 20 years on a simple interest rate ‘R’, then what is the rate of interest (value of R)?

(a) 30%    (b) 25%    (c) 20%    (d) 15%    (e) None of these

Ans: (b) 25%

Explanation:

Rate of interest = SI × 100/  Pn           (here, SI = 3600 – 600 = 3000)

                         = 3000 × 100/ 600 × 20 = 25%. Ans.

Q. 18. The simple interest on a certain sum of money for 2 years at 8% per annum is Rs.2200. What will be the compound interest at the same rate and for the same time?

(a) Rs.2248    (b) Rs.2268    (c) Rs.2278     (d) Rs.2288   (e) None of these

Ans: (d) Rs.2288

Explanation:

The Principal = SI × 100/ r n

                       = 2200 × 100/8 × 2 = Rs.13750.

CI = P (1+ r/100)ⁿ  - P

     = 13750 ( 1+ 8/100)² - 13750 = 13750 × 108/100 × 108/100 – 13750

    = 13750 × 1.08 × 1.08 – 13750 = 16038 – 13750 = Rs.2288. Ans.

Q. 19. The simple interest on Rs.7300 from 11 May, 1987 to 11 September, 1987 at 5% per annum is

(a) Rs.123    (b) Rs.103     (c) Rs.200    (d) Rs.223     (e) None of these

Ans: (a) Rs.123

Explanation:

SI = P r n/100

The no. of days = 20 + 30 + 31+ 31 +11 =123 out of 365 days 

   (the on which the money is invested will not be taken in to count)

Therefore, term = 123/365

So, S I = 7300 × 123 × 5/365 × 100 = Rs.123. Ans.

Q.20. The time in which Rs.2000 will amount to Rs.2420 at 10% per annum compound interest is

(a) 5 years   (b) 2 years   (c) 3 years    (d) 4 years    (e) None of these

Ans: (b) 2 years

Explanation:

The Amount (A) = P (1 + r/100 )ⁿ

i.e. 2420 = 2000 ( 1 + 10/100)ⁿ  = 2000 × (110/100)ⁿ  = 2000 × ( 11/10)ⁿ

(11/10)ⁿ    = 2420/2000 = 121/100 = (11/10)²

Therefore, n = 2   i.e. term = 2 years. Ans.

Q. 21. At what rate per cent of simple interest will a sum of money double itself in 12 years?

(a) 8 1/3%   (b) 8 ½ %       (3) 8 ¼ %      (d) 9 1/3%    (e) None of these

Ans: (a) 8 1/3%

Explanation:

When an amount doubles itself, then the Rate of interest = 100/term    and term = 100/ rate.

Therefore, here the rate of interest =  100/12 = 8 1/3%. Ans.

Q. 22. What would be the compound interest obtained on an amount of Rs.6650 at the rate of 14 p.c.p.a. after two years?

(a) Rs.2169.24    (b) Rs.1992.34     (c) Rs.2042.46     (d) Rs.1862.0     (e) None of these

Ans: (b) Rs.1992.34

Explanation:

Compound Interest =  P ( 1 + r/100 )ⁿ –P

              = 6650 ( 1 + 14/100 )² - 6650    = 6650 ×114/100 × 114/100 – 6650

                                                                = 6650 × 1.14 × 1.14 – 6650 = Rs.8642.34 – 6650

                                                                                                              = Rs.1992.34. Ans.

Q. 23. The simple interest accrued on an amount of Rs.84000 at the end of three years is Rs.30240. What would be the compound interest accrued on the same amount at the same rate in the same period?

(a) Rs.30013.95    (b) Rs.31013.95    (c) Rs.32013.95     (d) Rs.33013.95   (e) None of these

Ans: (e) None of these

Explanation:

The Rate of interest = SI × 100/ P n    = 30240 × 100/84000 × 3 = 12% p.a.

C I = P ( 1+ r/100 )ⁿ –P

      = 84000 ( 1 + 12/100)³ - 84000 = 84000 × 1.12 × 1.12 × 1.12 – 84000

    = 118013.952 – 84000 = Rs.34013.95. Ans.

Q. 24. The difference between the simple and compound interest on a certain sum of money for 2 years at 4% per annum is Re.1. The sum is

(a) Rs.2500   (b) Rs.2400  (c) Rs.2600    (d) Rs.2000    (e) None of these

Ans: (e) None of these

Explanation:

When the difference between C I and S I is given for 2 years,

then the Sum = difference ( 100/r)²

                    = 1 ( 100/4)² = 25² = Rs.625. Ans.

Q. 25. What approximate amount of compound interest can be obtained on an amount of Rs.3080 at the rate of 7 p.c.p.a. at the end of 3 years?

(a) Rs.586    (b) Rs.693   (c) Rs.646   (d) Rs.596     (e) Rs.621

Ans: (b) Rs.693

Explanation:

C I = P ( 1+ r/100 )ⁿ – P

     = 3080 ( 1 + 7/100 )³ - 3080 = 3080 × 1.07 × 1.07  × 1.07 – 3080 = 3773.13244 – 3080

                                                   = 693.13244 = Rs. 693. Approximately. Ans.

Q. 26. Mr. Deepak invested an amount of Rs.21250 for 6 years. At what rate of simple interest will he obtain the total amount of Rs.26350 at the end of 6 years?

(a) 6 p.c.p.a    (b) 5 p.c.p.a.   (c) 8 p.c.p.a.    (d) 12 p.c.p.a.   (e) none of these

Ans: (e) None of these

Explanation:

S I = 26350 – 21250 = Rs.5100

Rate = S I × 100/ P n

        = 5100 × 100/21250 × 6 = 4% p.a. Ans.

Q. 27. The difference between simple and compound interests on a sum of money at 4% per annum for 2 years is Rs.8. The sum is

(a) Rs.400   (b) Rs.800    (c) Rs.4000   (d) Rs.5000    (e)None of these

Ans: (d) Rs.5000

Explanation:

When the difference in SI and CI is given for 2 years, then the sum = difference × ( 100/r)²

                                     = 8 × ( 100/4)²   = 8 × 25 × 25 = Rs.5000. Ans.

Q. 28. A sum of money becomes eight times of itself in 3 years at compound interest. The rate of interest per annum is

(a) 100%    (b) 80%    (c) 20%    (d) 10%    (e) None of these

Ans: (a) 100%

Explanation:

i.e.     P( 1 + r/100)³ = 8P

             (1+ r/100)³ =8 = 2³

So, 1 + r/100 = 2    and  r/100 = 2 – 1 =1

Then, r = 100%. Ans.

Q. 29. The Compound interest on a certain sum for 2 years is Rs.412 and the simple interest is Rs.400. What is the rate of interest per annum?

(a) 3%   (b) 4%    (c) 6%   (d) 8%    (e) 5%

Ans: (c) 6%

Explanation:

In C I, the simple interest for the previous year is added to the principal and the interest for this amount is also included in the interest of the current year.

Thus,  the difference 412 -400 = Rs.12 is the interest for the first years S I at the same rate of interest.

Here, the first year’s SI = 400/2 = Rs.200

Rs. 12 is the interest  for Rs.200 in one year.

So, the rate of interest = SI × 100/ P n

                                    = 12 × 100/ 200 × 1 =  6% p.a. Ans.

Q. 30.  A certain sum of money is put on simple interest at a certain rate for 4 years. Had it been put at 3 % higher rate, it would have fetched Rs.360 more. What is the amount?

(a) Rs.2400   (b) Rs.3000   (c) Rs.3600    (d) Rs.4200   (e) None of these

Ans: (b) Rs.3000

Explanation:

At 3% more rate, the increase in SI for the 4 years = Rs.360

So, the increase in S I for 1 year = 360/4 = Rs.90

Rs.90 is 3% of the sum. 

So,1% of the sum = 90/3

Therefore, the sum = 90 × 100/3 = Rs.3000. Ans.

OR

Let ‘x’ be the sum and ‘r’ the rate percent per annum.

Then, x (r + 3) × 4/100 – x × r × 4/100 = 360

i.e. x ( r + 3) × 4 – x × r × 4  = 360 × 100

 4x ( r +3) – 4xr = 36000     i.e. 4xr + 12x – 4xr = 36000

 12x = 36000     and therefore, x = 36000/12 = Rs.3000. Ans.

Q. 31. What will be the difference between the simple and the compound interest at the rate of 15% per annum on a sum of Rs.12000 after 3 years?

(a) Rs.875    (b) Rs.900   (c) Rs.800.3     (d) Rs.860.5   (e) Rs.850.5

Ans: (e) Rs.850.5

Explanation:

If the Sum of money invested, the Rate percent and the Term are given and is asked to find the difference between the C I and S I is calculated as:

                 Difference = Sum × r² (300 + r)/ (100)³

Therefore, the required difference = 12000 × 15² (300 + 15)/ 100³

                                                       = 12000 × 225 × 315/1000000

                                                       = Rs.850.5. Ans.

Q. 32. A sum was put at simple interest at a certain rate for 10 years. Had it been put at 5% higher rate it would have fetched Rs.600 more. What was the sum?

(a) Rs. 2400   (b) Rs.2000    (c) Rs.1800   (d) Rs.1200      (e) None of these

Ans: (d) Rs.1200

Explanation:

At 5% more rate, the increase in SI for 10 years = Rs.600     (given)

So, at 5% more rate, the increase in SI for 1 year = 600/10 = Rs.60/-

i.e. Rs.60 is 5% of the invested sum

So, 1% of the invested sum = 60/5

Therefore, the invested sum = 60 × 100/5 = Rs.1200. Ans.

Q. 33. In what time will Rs.4200 amount to Rs.4898.88 at 16% compound interest payable half-yearly?

(a) 1 Year   (b) 2 years   (c) 1.5 years    (d) 2.5 years      (e) 3 years

Ans: (a) 1 year

Explanation:

For CI payable at half-yearly, the Amount = P ( 1+ r/2/100)²ⁿ

i.e. 4200 ( 1+ 16/2/100)²ⁿ = 4898.88

 i.e. 4200 (1 + 8/100) ²ⁿ = 4898.88

      4200( 1+ 2/25)²ⁿ  = 4898.88

i.e.   (27/25)²ⁿ = 4898.88/4200 = 489888/420000 = 729/625 = (27/25)^{2 × 1}

i.e. (27/25)²ⁿ  = (27/25)^{2 × 1}

therefore the time ‘n’ = 1 year. Ans.

Q.34. What would be the compound interest obtained on an amount of Rs.6875 at the rate of 8% p.a. after two years?

(a) Rs.948   (b) Rs.1024     (c) Rs. 1144    (d) Rs.1216     (e) None of  these

Ans: (c) Rs.1144

Explanation:

At CI, the Amount A = P ( 1+ r/100)ⁿ        and CI = A - P

So,  A = 6875 (1+ 8/100)² = 6875 ( 108/100)² = 6875 × 1.08 × 1.08 = Rs.8019

Therefore, CI = 8019 – 6875 = Rs.1144. Ans.

Q. 35. What should be the simple interest obtained on an amount of Rs.2800 at the rate of 16% p.a. after 3 years?

(a) Rs.1144    (b) Rs. 1244    (c) Rs.1344    (d) Rs.1444   (e) None of these

Ans: (c) Rs. 1344

Explanation:

S I = P r n/100

 = 2800 × 16 × 3/100 = 28 × 16 × 3 = Rs.1344. Ans.

Q. 36. What approximate amount of compound interest can be obtained on an amount of Rs.1542 at the rate of 4 p.c.p.a. after 2 years?

(a) Rs.126    (b) Rs.130    (c) Rs.122    (d) Rs.115   (e) Rs.135

Ans: (a) Rs.125

Explanation:

C I = P ( 1 + r/100)ⁿ – P

      = 1542 ( 1 + 4/100)² – 1542

     = 1542 × 104/100 × 104/100 – 1542

    = 1542 × 1.04 × 1.04 – 1542   = 1667.8272 – 1542 = Rs.126 approximately. Ans.

Q. 37. What will be the difference between the compound interest and simple interest at the rate of 5 p.c.p.a. on an amount of Rs.4000 at the end of two years?

(a) Rs.10    (b) Rs.20   (c) Rs.25      (d) Data inadequate    (e) None of these

Ans: (a) Rs.10.

Explanation:

If Sum invested, rate % and time is given, then the difference between CI and SI can be calculated as:

  Difference = Sum ( r/100 )²

                    = 4000 ( 5/100)² = 4000 × (1/20)²

                   = 4000 × 1/400 = Rs.10. Ans.  

Q. 38.    Amount of simple interest accrued on an amount of Rs.28500 in seven years is Rs.23940. What is the rate of interest p.c.p.a.?

(a) 10.5     (b) 12.5    (c) 11     (d) 12     (e) None of these

Ans: (d) 12

Explanation:

Rate percent = S I × 100/ P × Term

                     = 23940 × 100/28500 × 7 = 12%. Ans.

Q. 39. What is the compound interest accrued on an amount of Rs.8500 in two years @ interest 10 p.c.p.a.?

(a) Rs.1875     (b) Rs.1885    (c) Rs.1775    (d) Rs.1765    (e) None of these

Ans: (e) None of these

Explanation:

C I = P ( 1+ r/100)ⁿ – P

      = 8500 ( 1 + 10/100)² - 8500 = 8500 ( 110/100)² - 8500

                                                    = 8500 × 11/10 × 11/10 – 8500

                                                    = 85 × 11 × 11 – 8500 = 10285 – 8500 = Rs.1785. Ans.

Q. 40. The S I on a certain sum of money for 2 years at 8% per annum is Rs.300. What will be the C I (in Rs.) at the same rate and for the same time?

(a) 308    (b) 312    (c) 316   (d) 324   (e) None of these

Ans: (b) 312

Explanation:

Principal P  = S I × 100/r n

                   = 300 × 100/8 × 2 = Rs.1875

C I = P ( 1+ r/100)ⁿ – P

      = 1875 ( 1 + 8/100 )² - 1875

      = 1875 × 108/100 × 108/100 – 1875

      = 2187 – 1875 = Rs.312. Ans.

Q. 41. The simple interest on a sum of money is ¼ of the principal, and the number of years is equal to the rate % p.a. What will be the rate per cent?

(a) 5%  (b) 4%   (c) 16%   (d) 8%   (e) 10%

Ans: (a) 5%

Explanation:

Let the Sum invested, i.e. P, be ‘Rs.100’

Then, SI = 100 × ¼ = Rs.25.

The rate of interest p.a. = No. of years i.e. term and let it be ‘a’

Rate = S I × 100/ P n

Here, rate and time are equal, can take it as n r = a²

So, a² = SI × 100/ P

     a² = 25 × 100/100     

    a² = 25       a = 5

Therefore, the rate per cent p.a. = 5%. Ans.

Q. 42. Tannu invests an amount of Rs.9535 at the rate of 4% p.a. to obtain a total amount of Rs.11442 on simple interest after a certain period. For how many years did she invest the amount to obtain the total sum?

(a) 4 years   (b) 5 years   (c) 7 years   (d) 3 years   (e) None of these

Ans: (b) 5 years

Explanation:

Given,  S I = 11442 – 9535 = Rs.1907

Term = S I × 100/P r     = 1907 × 100/9535 × 4 = 5 years. Ans.

Q. 43. Mohan invests an amount of Rs.7690 at the rate of 7% p.a. for 2 years. What approximate amount of compound interest will be obtained after 2 years?

(a) Rs.1114     (b) Rs.1118     (c) Rs.2114      (d) Rs.1211     (e) None of these

Ans: (a) Rs.1114

Explanation:

C I = P ( 1 + r/100)ⁿ – P

 C I = 7690 ( 1 + 7/100)² - 7690

       = 7690 × 107/100 × 107/100 – 7690

       = 7690 × 1.07 × 1.07 – 7690 = 8804.281 – 7690 = Rs.1114. Approx. Ans.

Q. 44. A man deposits Rs.1000 in one bank at 8% p.a. and Rs.3000 in another bank at rate of 4% p.a.  Find the rate of interest for the whole sum.

(a) 5%   (b) 6%    (c) 7%    (d) 7.5%    (e) None of these

Ans: (a) 5%

Explanation:

S I = P n r/100

First S I = 1000 ×1 × 8 /100                        ( time can be taken as 1 year)

              = Rs.80

Second S I = 3000 × 1 × 4/100 = Rs.120

So, the total Principal = 1000 + 3000 = Rs.4000

       The S I                 =Rs. 80 + 120 = Rs.200

Then, the required rate of interest =  S I × 100/ P n

                                                      = 200 × 100/4000 × 1 = 5%. Ans.

Q. 45. If the difference between C I and S I on a certain sum of money for three years at 5% per annum is Rs.61, what is the sum (in Rs.)?

(a) 16000  (b) 12000   (c) 10000  (d) 8000    (e) 6000

Ans: (d) 8000

Explanation:

If difference between C I and S I, rate% and time is given, then we can find the Sum invested as:

Sum = Difference × 100³/r² (300 + r)

        = 61 × 100 × 100 × 100/5×5 × 305 = 40000/5 = Rs.8000. Ans.

Q. 46. Raviraj invested an amount of Rs.10000 at compound interest rate of 10 p.c.p.a. for a period of three years. How much amount will Raviraj get after three years?

(a) Rs.12310   (b) Rs.13210   (c) Rs.13320    (d) Rs.13120    (e) None of these

Ans. (e)  None of these

Explanation:

Amount ‘A’ = P (1+ r/100)ⁿ

                    = 10000 ( 1 + 10/100)³

                  = 10000 × 110/100 × 110/100  × 110/100 = Rs.13310. Ans.

Q. 47. Simple interest on a certain sum at the rate of 20% per annum for a period of 8 years amounts to Rs.10960. What is the original sum of money?

(a) Rs.6500   (b) Rs.7800    (c) Rs.8000   (d) Data inadequate  (e) None of these

Ans: (e) None of these

Explanation:

The original Sum, i.e. P = SI × 100/ r n

                                       = 10960 × 100/ 20 × 8 = Rs.6850.Ans.

Q. 48. The difference between the simple interest on a certain sum of money at 6% per annum for 10 years and at 5% per annum for 2 years is Rs.100. Find the sum.

(a) Rs.100   (b) Rs.200   (c) Rs.400  (d) Rs.500    (e)None of these

Ans: (b) Rs.200.

Explanation:

Let the Sum be ‘P’

S I = P r n /100

So,       P × 6 × 10/100 – P × 5 × 2/100 = Rs.100

          i.e. 60 P – 10P = 100 × 100

                50P = 10000

Therefore. The Sum P = 10000/50 = Rs.200.Ans.

Q. 49. The difference between the simple interest and the compound interest (compounded annually) at the rate of 12% per annum on Rs.5000 for two years will be

(a) Rs.17.50    (b)Rs.36   (c) Rs.45   (d) Rs.72     (e) None of these

Ans: (d) Rs.72

Explanation:

When the Sum invested, the rate of interest per annum and for 2 years,

the difference between S I and C I can be calculated as:

 Difference = Sum ( r/100 )²

                 = 5000 (12/100)² =  5000 × 12/100 × 12/100 = Rs.72.Ans.

Q. 50. In how many years a certain sum doubles itself at 4% per annum simple interest?

(a) 5 years   (b) 10 years    (c) 20 years   (d) 25 years    (e) none of these

Ans: (d) 25 years

Explanation:

When a Sum doubles itself, then, the rate percent, ‘r’ = 100/n and the term (time) ‘n’ =100/r.

Therefore the required time = 100 /r  = 100/4 = 25 years. Ans.

Q. 51. What is the difference between the simple and the compound interest on Rs.400 for 2 years at 5% p.a.

(a) Rs.5   (b) Rs.4   (c) Rs.3    (d) Rs.2     (e) None of these

Ans: (e) None of these

Explanation:

The difference between the S I and CI for 2 years = Sum ( r/100)²

                                                                                = 400 (5/100)² = 400 × 5/100 × 5/100

                                                                                = Rs.1. Ans.

Q.  52. In what time will Rs.1000 amount to Rs.1331 at 20% per annum, compounded half-yearly?

(a) 1 ½ years    (b)  2 years    (c) 1 year   (d) 2 ½ years   (e) None of these

Ans: (a) 1 ½ years

Explanation:

For CI payable at half-yearly, the Amount = P ( 1+ r/2/100)²ⁿ

       Rs.1331  = 1000(1+r/2/100)²ⁿ

            1331 = 1000 × (110/100)²ⁿ

                 1331 = 1000 × (11/10)²ⁿ

             (11/10)²ⁿ = 1331/1000 =  (11/10)³

Therefore, 2n = 3;    n = 3/2 = 1 ½ years. Ans.

Q.53. What approximate amount of compound interest can be obtained on an amount of Rs.2575 at the rate of 5% p.a. at the end of 2 years?

(a) Rs.224   (b) Rs.236   (c) Rs.248     (d) Rs.264   (e) None of these

Ans: (d) Rs.264

Explanation:

C I = P (1+ r/100)ⁿ – P

      = 2575 ( 1 + 5/100)² - 2575 = 2575 (105/100)² -2575

      = 2575 × 1.05 × 1.05 – 2575 = 2838.9375 – 2575

      = Rs.263.9 = Rs.264 Approx. ans.

Q.54. A sum of money at simple interest amounts to Rs.1012 in 2 ½ years and to Rs.1067.20 in 4 years. The rate of interest per annum is

(a) 2.5%    (b) 3%    (c) 4%     (d) 5%    (e) None of these

Ans: (c) 4%

Explanation:

 Amount, A = P + S I for 2 ½ years = Rs.1012

Amount for 4 years = Rs.1067.20.

Therefore, S I for 1 ½ years = Rs.1067.20 – Rs.1012 = Rs.55.20

So, S I for 2 ½ years = 55.20 ÷ 3/2 × 5/2  = 55.20 × 2/3 × 5/2 = Rs.92.

Therefore, the Principal = Amount – S I = 1012 – 92 = Rs.920.

Rate of interest = S I × 100/P n

                         = 92 × 100/920 × 5/2 = 92 × 100 × 2 / 920 × 5 = 4%. Ans.

Q. 55. If the compound interest on a sum for 2 years at 12 ½% per annum is Rs.510, the simple interest on the same sum at the same rate for the same period of time is

(a) Rs.400   (b) Rs.480    (c) Rs.450      (d) Rs.460    (e) None of these

Ans: (b) Rs.480.

Explanation:

If the C I, the rate of interest(r) and  term (n) is given,

We can calculate the Simple Interest as:

S I = r n × C I/100 [ (1 + r/100)ⁿ – 1]

 i.e. Simple Interest = 25/2 × 2 × 510/ 100[(1 + 25/2/100)² - 1] = Rs.480 approx. Ans.

Q. 56. In 4 years, the simple interest on a certain sum of money is 9/25 of the principal. The annual rate of interest is

(a) 4%    (b) 4 ½%   (c) 9%   (d) 10%     (e) None of these

Ans: (c) 9%

Explanation:

Let ‘P’ be the principal and ‘r’ the rate of interest

Then,    P r × 4/100 = 9P/25

             P r × 4 × 25 = 9 × 100 P

                Then, r = 900/100 = 9%. Ans.

Q. 57. A sum of money invested at compound interest amounts to Rs.800 in 3 years and to Rs.840 in 4 years. The rate of interest per annum is

(a) 2 ½%   (b) 4%    (c) 5%    (d) 6 2/3%      (e) None of these

Ans: (c) 5%

Explanation:

Given, CI for 3 years = Rs.800

           CI for 4 years = Rs.840

 Therefore, CI for 3 rd year, i.e. for the principal Rs.800 = 840 -800 = Rs.40

i.e. Rs.40 is the simple interest for Rs.800

then, the rate of interest = 40 × 100/800 = 5%. Ans.

Q. 58. The difference between simple and compound interest on a certain sum of money for 2 years at 4 per cent per annum is Re.1. The sum of money is

(a) Rs.600     (b) Rs.625    (c) Rs.560    (d) Rs.650    (e) None of these

Ans: (b) Rs.625

Explanation:

If the difference between CI and SI, and the rate of interest for 2 years is given, then the Sum invested can be calculated as:

Sum = Difference (100/r)² = 1 (100/4)² = Rs.625. Ans.

Q. 59. What sum of money will become Rs.1352 in 2 years at 4 per cent per annum compound interest?

(a) Rs.1200   (b) Rs.1225     (c) Rs.1250     (d) Rs.1300    (e) None of these

Ans: (c) Rs.1250

Explanation:

The Amount A = P ( 1+ r/100)ⁿ

      i.e. 1352 = P ( 1 + 4/100)²

            1352 = P ( 104/100)²

            1352 = P ( 26/25)² = P × 26/25 × 26/25

              P = 1352 /26/25 × 26/25 = 1352 × 25 × 25/26 ×26

                 =Rs.1250.Ans.

Q. 60. A certain sum of money amounts to Rs.756 in 2 years and to Rs.873 in 3 ½ years at a certain rate of simple interest. The rate of interest per annum is

(a) 10%   (b) 11%    (c) 12%    (d) 13 %     (e) None of these

Ans: (d) 13%

Explanation:

Given, the  amount for 2 years =Rs.756

            The amount for 3 ½ years = Rs.873

Therefore, S I for 1 ½ years = 873 – 756 = Rs.117

Therefore, S I for 2 years = 117 / 1 ½  × 2 = 117 / 3/2 ×2

                           = 117 × 2 × 2/3 = Rs.156

         Therefore, the Sum = Rs.756 – 156 = Rs.600.

So, the rate per cent = SI ×100/P r   = 78 × 100/600 × 1 = 78/6 = 13%. Ans.

Q. 61. A certain part of an amount of Rs.7200 was lent at 8% p.a. and the remaining at 12% p.a. If the total simple interest from both the parts in four years was Rs.2944, what is the amount which was lent at 8% p.a. interest?

(a) Rs.3200    (b) Rs.3500   (c) Rs. 3600   (d) Rs.4000     (e) Rs.4800

Ans: (a) Rs.3200

Explanation:

Let the principal lent on 8% interest rate p.a = ‘x’

We know that, S I = p n r/100

Then,      8 × 4 × x/100 + ( 7200 – x) 12 × 4/100 = Rs. 2944

  i.e.   32x + 345600 – 48x = 294400

          345600 – 294400 = 48x -32x

            51200 = 16x

Therefore,  x = 51200/16 = Rs.3200. Ans.

Q. 62. A person lent a certain sum of money at 8% simple interest and in 8 years the interest amounted to Rs.216 less than the sum lent. What is the sum that the person lent?

(a) Rs.1800    (b) Rs.1200    (c) Rs.800     (d) Rs.600     (e) None of these

Ans: (d) Rs.600

Explanation:

Let ‘P’ be the sum or principal

P = S I × 100/ r n

Given, S I = P – 216

So, P =  (P – 216) × 100/8 × 8

i.e.    64 P = 100P – 21600

21600 = 100P – 64 P = 36P

P = 21600/36 = Rs.600. Ans.

Q. 63. Equal amounts are deposited in two banks each at 3.5% p.a. for 12 years and 8.5 years respectively. If the difference between their interests is Rs.189.875 then what is the amount?

(a) Rs.1550    (b) Rs.1650    (c)Rs.1750     (d) Rs.1850     (e) Rs.1950

Ans: (a) Rs.1550

Explanation:

Let the principal amount be ‘P’

We know that, S I = P n r/100

Then,   P × 12 × 3.5/100 – P × 8.5 × 3.5/100 = Rs.189.875

           42P/100 – 29.75P/100 = 189.875

          12.25P = 189.875 × 100 = 18987.5

           P = 18987.5/12.25 = Rs.1550.Ans.

Q. 64. A  certain amount becomes Rs.627200 in two years and Rs.702464 in three years. If the interest is compounded yearly what is the rate of interest?

(a) 11%    (b) 12%    (c) 13%     (d) 14%    (e) 15%

Ans: (b) 12%

Explanation:

C I for the third year = Rs.702464 – Rs.627200 = Rs.75264

Rs.75264 is the SI for I year for Rs.627200.

Therefore, the Rate of interest = SI × 100/P n        (here, n = 1 year)

   i.e. 75264 × 100/627200 × 1 = 75264/6272 = 12% Ans.

Q. 65. What is the compound interest accrued on a sum of Rs.1800 at the rate of 4 p.c.pa. in 2 years?

(a) Rs.146.88    (b) Rs.1946.88   (c) Rs.156.84     (d) Rs.1846.84    (e) None of these

Ans: (a) Rs.146.88

Explanation:

 C I = P (1 + r/100)ⁿ – P

       = 1800 ( 1+ 4/100)² - 1800 = 1800 × 1.04 × 1.04 – 1800

       = 1946.88 – 1800 = Rs.146.88.Ans.

Q. 66. The simple interest accrued on a certain principal in 5 years at the rate of 12 p.c.pa.  is Rs.1536. What amount of the simple interest would one get if one invests Rs.1000 more than the previous principal for 2 years and at the same rate pc.p.a.?

(a) Rs.845.40    (b) Rs.614.40    (c) Rs.2136      (d) Rs.1536   (e) None of these

Ans: (e) None of these

Explanation:

 P = S I ×100/ r n

    = 153600/60 = Rs.2560

P + 1000 = 2560 + 1000 = Rs.3560

Then, the SI for 2 years on Rs.3560 at 12 p.c.p.a

          S I = P r n/100

               = 3560 × 12 × 2/100 = Rs.854.40. Ans:

Q. 67. A person lent a certain sum of money at 8% simple interest and in eight years, the interest amounted to Rs.635.40 less than the amount lent. What is the amount the person lent?

(a) Rs.1725      (b) Rs.1735     (c) Rs.1745     (d) Rs.1755      (e) Rs.1765

Ans: (e) Rs.1765

Explanation:

Let the sum of money be ‘P’

SI = P n r/100

    = P × 8 × 8/100    = 16P/100

P -16P/100 = Rs.635.40

25P – 16P = Rs.635.40 × 25

9P = 15885

P = 15885/9 = Rs.1765. Ans.

Q. 68. An amount of Rs.14800 becomes Rs.26973 after two years at compound interest. What is the rate of interest?

(a) Rs.55%   (b) 45%   (c) 35%    (d) 25%      (e) 15%

Ans: (c) 35%

Explanation:

A = P (1+ r/100)ⁿ 

26973 = 14800 (1+ r/100)²

( 1+ r/100)² = 26973/14800

(1+ r/100)² = 26973/14800

1 + r/100 = √26973/14800 = 13.5/10 = 1.35

r/100 = 1.35 – 1 = 0.35

r = 0.35 × 100 = 35%. Ans.

Q. 69. If the difference between the compound interest and the simple interest earned on a sum of money at the rate of 20% p.a. for two years is Rs.24, what is the amount?

(a) Rs.400   (b) Rs.600   (c) Rs.800     (d) Rs.1200   (e) None of these

Ans: (b) Rs.600

Explanation:

When the difference between CI and SI, and rate of interest for 2 years is given, we can find the sum invested as:

Sum = Difference ( 100/r)²

        = 24 ( 100/20)²  = 24 × 25 = Rs.600. Ans.

Q. 70. What is the difference between the Compound interest and the simple interest for an amount  of Rs.15000 at 12% p.a. for 2 years?

(a) Rs.312   (b) Rs.288   (c) Rs.232   (d) Rs.216   (e) None of these

Ans: (d) Rs.216.

Explanation:

When the Sum invested and the rate of interest per annum  for 2 years are given, then we can calculate the difference between CI and SI as:

Difference = Sum (r/100)²

                  = 15000 ( 12/100)² = 1.5 ×144 = Rs.216. Ans.

Q. 71. The difference between the interest received from the two different banks on Rs.960 for 4 years is Rs.28.8, then what is the difference between their rates ?

(a) 3.5%  (b) 1.25%   (c) 0.75%    (d) 0.5%    (e) 0.25%

Ans: (c) 0.75%

Explanation:

Simple Interest ( SI) = P r n/100

Here, SI₁ = 960 × 4 × r₁/100 = 38.4 r₁

        Similarly, SI₂ = 38.4r₂

Given, SI₁ – SI₂ = Rs.28.8

        i.e. 38.4 r₁ – 38.4 r₂ = 28.8

 38.4 ( r₁ – r₂) = 28.8

 So,  r₁ – r₂  = 28.8/38.4 = 0.75%. Ans.

Q. 72. Vinitha invested a certain amount at the rate of 8 p.c.p.a. for 5 years and obtained a simple interest of Rs.3800. Had she invested the same amount at the same rate of interest for 2 years, how much amount would she have obtained as compound interest at the end of 2 years?

 (a) Rs.1580.80   (b) Rs.1520    (c) Rs.1550.50    (d) Rs.1550   (e) None of these

Ans: (a) Rs.1580.80

Explanation:

The Principal P = SI × 100/ r n

                         = 3800 × 100/ 8 × 5 = Rs.9500

C I = P (1 + r/100)ⁿ – P

      = 9500 ( 1 + 8/100)² - 9500

 = 9500 × 1.08 × 1.08 – 9500

= 11080.8 – 9500 = Rs.1580.80. Ans.

Q. 73. What would be the compound interest obtained on an amount of Rs.6000 at the rate of 10% p.a. after 3 years?

(a) Rs.1800  (b) Rs.1836   (c) Rs.1946    (d) Rs.1986    (e) Rs.1994

Ans: (d) Rs.1986

Explanation:

Compound Interest  C I = P ( 1+ r/100)ⁿ – P

       = 6000 ( 1 + 10/100)³ - 6000

       = 6000 × 1.1 × 1.1 × 1.1 – 6000 = 7986 – 6000 = Rs.1986. Ans.

Q. 74. Rs.540 becomes Rs.891 in five years when the interest is simple. If the rate of interest is increased by 2% then what will be the total amount after four years?

(a) Rs.904    (b) Rs.896    (c) Rs.872     (d) Rs.864     (e) None of these

Ans: (d) Rs.864

Explanation:

The S I for 5 years given = Rs.891 – Rs.540 = Rs.351

Then the rate of interest = S I × 100/ P n

                                       = 351 × 100/540 × 5

                                      = 13%.

After increase of 2% the new rate of interest = 15%

S I at this rate for 4 years = 540 × 15 × 4/100 = Rs.324

Therefore, the amount = P + S I = Rs.540 + Rs.324 = Rs.864. Ans.

Q. 75. The simple interest accrued in 3 years on a principal of Rs.25000 is three – twentieths the principal. What is the rate of simple interest p.c.p.a.?

(a) 5    (b) 4    (c) 6      (d) 3      (e) None of these

Ans: (a) 5%

Explanation:

Simple Interest SI = P × 3/20 = 25000 × 3/20 = Rs.3750

Rate of interest r = SI × 100/P n

                            = 3750 × 100/25000 × 3 = 5%. Ans.

Q. 76. The difference between the interest received from two different banks on Rs.1500 for four years is Rs.75. Find the difference between their rates

(a) 0.25%    (b) 0.5%   (c) 0.75%      (d) 1%     (e) 1.25%

Ans: (e) 1.25%

Explanation:

Let ‘r₁’ and ‘r₂’ be the two rates of interest.

Then, S I = P r n/100

So, SI_{1 =}  1500 × 4 × r₁/100 = 60r₁

 And  S I ₂ = 60r₂

Given, SI₁ – SI₂ = Rs.75

i.e. 60r₁ – 60r₂ = 75

60(r₁ – r₂) = 75

 So, r₁ – r₂ = 75/60 =5/4 = 1.25%. Ans.

Q. 77. If the difference between the compound interest and the simple interest on a certain sum of money for three years at 30% p.a. is Rs.8316, what is the sum?

(a) Rs.24000    (b) Rs.28000   (c) Rs.32000   (d) Rs.36000  (e) None of these

Ans: (b) Rs.28000

Explanation:

When the difference between CI and SI, and rate of interest per annum for three years is given, then the Sum invested can be calculated as:

Sum = Difference × 100³/r² × (300 + r)

        = 8316 × 100 × 100 × 100/ 30 × 30 × 330

     = 8316 × 100 × 100 × 100/900 × 330 = Rs.28000. Ans.

Q. 78. Ravi borrowed some money at the rate of 4 pcpa for the first three years, at the rate of 8 pcpa for the next two years and at the rate of 9 pcpa for the period beyond 5 years. If he pays a total simple interest of Rs.19550 at the end of 7 years, how much money did he borrow?

(a) Rs.39500   (b) Rs.42500    (c) Rs.41900     (d) Rs.43000   (e) None of these

Ans: (b) Rs.42500

Explanation:

Let ‘P’ be the borrowed Sum.

SI = P r n/100

So, the total interest (SI)  i.e.  P × 4 × 3/100 + P × 8 × 2/100 + P × 9 × 2/100 = Rs.19550

                                        i.e. 12P + 16P + 18P/100 = 19550

                                        i.e. 46P = 19550 × 100

                                                  P = 19550 × 100/46

                                                     = Rs. 42500. Ans.

Q. 79. The simple interest of an amount of  Rs.8560 at the end of 5 years is Rs.5136. What is the rate of interest pcpa?

(a) 15%    (b) 12%   (c) 14%      (d) 10%       (e) 11%

Ans: (b) 12%

Explanation:

The rate of interest r = SI × 100/P n

                                  = 5236 × 100/8560 × 5 =  12%. Ans.

Q. 80. The compound interest on a certain sum for 2 years is Rs.82 and the simple interest is Rs.80. What is the rate of interest per annum?

(a) 2%    (b) 4%    (c) 8%    (d) 10%    (e) None of these

Ans: (e) None of these

Explanation:

The S I for 1 year =  80/2 = Rs.40

Difference between CI and SI for 2 years = 82 – 80 = RS.2

This Rs.2 is the SI for Rs. 40 ( the SI for the 1st year)

So, the rate percent = 2 × 100/40 = 5% Ans.

Q. 81. The sum of money that will give Rs.4 per day as simple interest at the rate of 8% per annum is36500

(a) Rs.9125    (b) Rs.18250   (c) Rs.27375   (d) Rs. 36500   (e) None of these

Ans: (b) Rs.18250

Explanation:

S I for  1 year  ( i.e. 365 days) = 365 × Rs.4 = Rs.1460

P = SI × 100/ r n

   = 1460 × 100/ 8 × 1 = Rs.18250. Ans.

Q. 82. What would be the simple interest obtained on an amount of Rs.8880 at the rate of 7.5% per annum after seven years?

(a) Rs.3211  (b) Rs.3672    (c) Rs.4424      (d) Rs.4662     (e) Rs.4880

Ans: (d) Rs.4662

Explanation:

S I = P r n /100

     = 8880 × 7.5 ×7/100 = 888 × 75 × 7/100 = Rs.4662. Ans.

Q. 83. How much will be the compound interest to be paid on a principal amount of Rs.53000 after 2 years at the rate of 4 pcpa?

(a) Rs.4324.8    (b) Rs.4432.8     (c) Rs.4342.8    (d) Rs.4234.8    (e) None of these

Ans: (a) Rs.4324.8

Explanation:

C I = P ( 1 + r/100)ⁿ – P

      = 53000 ( 1 + 4/100)² - 53000 = 53000 × 1.04 ×1.04 – 53000

      = 57324.8 – 53000 = Rs.4324.8. Ans.

Q. 84. The difference between the simple interest and the compound interest compounded every six months at the rate of 30% per annum, at the end of 1 ½ years is Rs.5670. What is the sum?

(a) Rs.40000    (b) Rs.60000     (c) Rs.64000      (d) Rs.72000   (e) Rs.80000

Ans: (e) Rs.80000.

Explanation:

C I = P[(1+ r/100)ⁿ -1]

S I = P r n /100

 Given, CI is compounded every six months, in this case r = 30/2 =15% and n =3 and

Let ‘P’ be the required sum,

Then,   P [(1+ 15/100)³ -1] – P × 30 × 1.5/100 = Rs.5670

i.e. P [ ( 1.15 × 1.15 × 1.15) – 1] – 0.45P = 5670

     P ( 1.520875 – 1) – 0.45P = 5670

P ( 0.520875 – 0.45) = 5670

P = 5670/0.70875 = RS.80000. Ans.

Q.  85. What will be the compound interest on a amount of Rs.12000, if the interest is compounded half- yearly at 20% per annum for 1 ½ years?

(a) Rs.3654    (b) Rs.3748   (c) Rs.3876     (d) Rs.3972     (e) Rs.4012

Ans: (d) Rs.3972

Explanation:

Rate of interest for 6 months = 20/2 = 15%

Term = 1 ½ years = 3 six months, So, n = 3

CI = P [( 1+ r/100)ⁿ – 1]

     = 12000 [ ( 1 + 10/100)³ - 1] = 12000 × 1.1 × 1.1 × 1.1 – 12000

                                                   = 15972 – 12000 = Rs.3972. Ans.

Q. 86. Ramesh invested an amount of Rs.100000 at compound interest rate of 5% pa for a period of 2 years. How much amount will Ramesh get after 2 years?

(a) Rs.110250    (b) Rs.110500   (c) Rs.110750    (d) Rs.120000    (e) None of these

Ans: (a) Rs.110250

Explanation:

Amount  A = P ( 1+ r/100)ⁿ

                   = 100000 ( 1+ 5/100)² = 100000 × 1.05 × 1.05 = Rs.110250. Ans.

Q. 87. What would be the simple interest obtained on an amount of Rs.7250 at the rate of 15 pcpa after 3 years?

(a) Rs.3125     (b) Rs.3262.5      (c) Rs.3375.5    (d) Rs.3475     (e) None of these

Ans: (b) Rs.3262.5

Explanation:

 S I = P n r /100

      = 7250 × 15 × 3/100 = Rs.3262.5. ans.

Q. 88. On what sum will the difference between simple interest and compound interest for 3 years at 20% pa amount to Rs.3840?

(a) Rs.25000     (b) Rs.30000       (c) Rs.32000   (d) Rs.36000   (e) Rs.40000

Ans: (b) Rs.30000

Explanation:

When the difference between CI and SI, rate of interest pa for 3 years is given,

Then the Sum can be calculated as:

 Sum = Difference × 100³/r² (300 + r)

          = 3840 × 100³/ 20² ( 300 + 20)

          =  3840 × 100 × 100 × 100/400 × 320

          = Rs.30000. Ans.

Q. 89. A sum of Rs.5250 is lent in two parts in such a way that the interest on the first part at 5% for 8 years is equal to that on the second part at 3% for 10 years. What is the difference between these two parts?

(a) Rs.600   (b) Rs.750    (c) Rs.800   (d) Rs.850    (e) None of these

Ans: (b) Rs.750

Explanation:

Let the two parts of the sum be ‘p₁ and p₂’ respectively, SI = p r n/100

Then, p₁ × 5 × 8/100 = p₂ × 3 × 10/100

i.e. 40 p₁ = 30 p₂

p₁/p₂ =30/40  = ¾ = 3 : 4

then,   p₁ = 5250 × 3/7 = Rs.2250

and p₂  = 5250 × 4/7 = Rs.3000

So, the difference between the two parts = 3000 – 2250 = Rs. 750. Ans.

Q. 90.   A certain sum of money grows up to Rs.125440 in two years and up to Rs.175616 in three years on compound interest. What is the rate of interest per annum?

(a) 5%    (2) 10%    (3) 20%    (d) 25%   (e) 40%

Ans: (e) 40%

Explanation:

The difference in amount i.e. Rs.175616 – 125440 = Rs.50176

Rs. 50176 is the S I for Rs. 125440 for 1 year.

Therefore, the rate of interest = SI × 100/ P n

                = 50176 × 100/ 125440 × 1

                = 40% . Ans.

Q. 91. A man gets a simple interest of Rs.1000 on a certain principal at the rate of 5 p.c.p.a. in 4 years. What compound interest will the man get on twice the principal in two years at the same rate?

(a) Rs.1050    (b) Rs.1005   (c) Rs.11025    (d) Rs.10125    (e) none of these

Ans: (e) none of these

Explanation:

The Principal P = SI × 100/ r n

            = 100000/20 = Rs.5000.

Twice the principal = Rs.10000

CI = P[ (1 + r/100)ⁿ -1]

     = 10000 [(1+ 5/100)² - 1]  = 10000 × 1.05 × 1.05 – 10000

      = 11025 – 10000 = Rs.1025. Ans.

Q. 92. A person lent some amount @ 12% p.a. simple interest, and after 8 years he interest amounted to Rs.312 less than the amount lent. What is the amount that person lent?

(a) Rs.7000   (b) Rs.7200   (c) Rs.7400     (d) Rs.7600     (e) Rs.7800

Ans: (e) Rs.7800

Explanation:

S I = P nr /100

Let the principal = P

S I = P × 8 × 12/100 = 24P/25

Then, P – 24P/25 = Rs.312

25P -24P = 312 × 25

P  = 312 × 25 = Rs.7800. Ans.

Q. 93. Rs. 7800 becomes Rs.12480 in five years when the interest is simple. If the rate of interest  is increased by 6% then what will be the total amount after five years?

(a) Rs. 14820    (b) Rs.14920     (c) Rs.15820    (d) Rs.16820    (e) Rs.17820

Ans: (a) Rs.14820

Explanation:

The rate of interest = SI × 100/P n

S I = Rs.12480 – Rs.7800 = Rs.4680

Then, r = 4680 × 100/ 7800 × 5 = 12%

The increased rate of interest = 12 + 6 = 18%

SI at 18% = 7800 ×18 × 5/100 = Rs.7020.

Then, the required Amount = 7800 + 7020 = Rs.14820. Ans.

Q.94. What approximate amount of compound interest  can be obtained on an amount of Rs.9650 at the rate of 6 p.c.p.a. at the end of 3 years?

(a) Rs.1737   (b) Rs.1920    (c) Rs.1720   (d) Rs.1860     (e) Rs.1843

Ans: (e) Rs.1843.

Explanation:

C I = P ( 1 + r/100 )ⁿ –P

      = 9650 ( 1 + 6/100)³ - 9650

      = 9650 × 1.06 × 1.06 × 1.06 – 9650

      = 11493 – 9650 = Rs.1843. approx. Ans.

Q. 95. Vikrant invested an amount of Rs.19845 at the rate of 6 p.c.p.a. for a certain period. After how many years will he obtain a simple interest of Rs.9525.6 on the given rate of interest?

(a) 8 years   (b) 5 years   (c) 6 years   (d) Cannot be determined   (e) None of these

Ans: (a) 8 years

Explanation:

Term or Time ‘n’ = S I × 100/ P r

                             = 9525.6 × 100/19845 × 6 = 8 years. Ans.

Q. 96. Mr. Phanse invests an amount of Rs.24200 at the rate of 4 p.c.p.a. for 6 years to obtain a simple interest . Later he invests the principal amount as well as the amount obtained as simple interest for another 4 years at the same rate of interest. What amount of simple interest will he obtain at the end of the last 4 years?

(a) Rs.4800  (b) Rs.4850.32   (c) Rs.4801.28    (d) Rs.4700   (e) None of these

Ans: (c) Rs.4801.28

Explanation:

S I = P r n/100

S I in the first case = 24200 × 4 × 6/100 = Rs.5808.

Amount = 24200 + 5808 = Rs.30008.

S I in the second case = 30008 × 4 × 4/100 = Rs.4801.28. Ans.

Q. 97. Ms. Khyati deposits an amount of Rs.68400 to obtain a simple interest at the rate of 18 p.c.p.a. for 4 years. What total amount will Ms.Khyati get at the end of 4 years?

(a) Rs.117648    (b) Rs.110284    (c) Rs.113334    (d) Rs.116472     (e) None of these

Ans: (a) Rs.117648

Explanation:

S I = P r n/100

     = 68400 × 18 × 4/100 = Rs.49248

The amount at the end of 4 years = P + SI = 68400 + 49248 = Rs.117648. Ans.

Q. 98. Sonia invested an amount of Rs.17500 at the rate of 8 p.c.p.a. After how many years will she obtain a simple interest of Rs.16800?

(a) 15 years   (b) 8 years   (c) 9 years   (d) 12 years   (e) None of these

Ans: (d) 12 years

Explanation:

Time ‘n’ = SI × 100/P r

               = 16800 × 100/17500 × 8 = 12 years. Ans.

Q. 99. The simple interest accrued on an amount of Rs.16500 at the end of three years is Rs.5940. What would be the compound interest accrued on the same amount at the same arate in the same period? (rounded  off to two digits after decimal?

(a) Rs.6681.31   (b)6218.27  (c) Rs.6754.82    (d) Rs.6537.47    (e) None of these

Ans: (a) Rs.6681.31

Explanation:

The rate of interest ‘r’ = SI × 100/ P n

                                    =5940 × 100/16500 × 3 = 12%

 C I = P (1 +r/100)ⁿ –P

       = 16500 (1+ 12/100)³ - 16500

       = 16500 × 1.12 × 1.12 × 1.12 – 16500 = 23181.302 – 16500 = Rs.6681.31. approx. Ans.

Q. 100. Sourabhi invested an amount of Rs.16840 at the rate of 6 p.c.p.a. for 5 years. What total amount will she obtain with the simple interest at the said rate at the end of 5 years?

(a) Rs.20984   (b) Rs.21764   (c) Rs.20584   (d) Rs.21892    (e) None of these

Ans: (d) Rs.21892

Explanation:

S I = P n r/100

     = 16840 × 5 × 6/100  = Rs.5052

The total amount at the end of 5 years =  P + SI = 16840 + 5052 = Rs.21892. Ans.