Aptitude Simple And Compound InterestPage 4
25. | | What will be the difference between simple and compound interest @ 10% par annum on a sum of Rs.1000 after 4 years ? | | (a)31 | | (b)32.10 | | (c)40.40 | | (d)64.10 |
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Answer is: DS.I. = Rs.(1000 x 10 x 4/100) = Rs.400.
C.I. = Rs.[1000 x (1 + 10/100)^4 -1000] = Rs.464.10.
∴ Difference = Rs.(464.10 - 400) = Rs.64.10
26. | | The difference between simple interest and compound on Rs. 1200 for one year @ 10% per annum reckoned half-yearly is ? | | (a)2.50 | | (b)3 | | (c)3.75 | | (d)4 |
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Answer is: BS.I. = Rs.(1200 x 10 x 1)/100
S.I. = Rs.120.
C.I. = Rs.[1200 x (1+5/100)² - 1200]
C.I. = Rs.123.
∴ Difference = Rs.(123-120) = Rs.3.
27. | | There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12000 after 3 years at the same rate ? | | (a)2160 | | (b)3120 | | (c)3972 | | (d)6240 |
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Answer is: CLet P = Rs.100. Then,
S.I. = Rs.60 and T = 6 years.
∴ R = 100 x 60/100 x 6 = 10% p.a.
Now, P = Rs.12000
T = 3 years and R = 10% p.a.
∴ C.I. = Rs.[12000 x {(1 + 10/100)³-1}]
C.I. = Rs. (12000X333/1000) = Rs. 3972.
28. | | The difference between compound interest and simple interest on an amount of Rs. 15000 for 2 years is Rs. 96. What is the rate of interest per annum ? | | (a)8% | | (b)10% | | (c)12% | | (d)cannot be determined(CBD) |
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Answer is: A[15000 x (1+R/100)²-15000]-(15000 x R x 2/100) = 96
⇔ 15000[(1+R/100)²-1-2R/100] = 96
⇔ 15000[(100+R)²-10000-200R] = 96
⇔ R² = 96 x 2/3 = 64
⇔ R = 8.
∴ Rate = 8%.
29. | | The difference between the simple interest on a certain sum at the rate of 10% per annum for 2 years and compound interest which is compounded every 6 months is Rs. 124.05. What is the principal sum ? | | (a)6000 | | (b)8000 | | (c)10,000 | | (d)12,000 |
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Answer is: BLet the sum be Rs. P.
Then P[(1+5/100)^4-1] - P x 10 x 2/100 = 124.05 (note: ^4 is the power of 4)
⇒ P[(21/20)^4 - 1 - 1/4] = 124.05
⇒ P[(194481/160000) - (6/5)] = 12405/100
⇒ P[194481-192000/160000] = 12405/100
⇒ P = [(12405/100) x (160000/2481)] = 8000
30. | | The effective rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is: | | (a)6.06% | | (b)6.07% | | (c)6.08% | | (d)6.09% |
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Answer is: DAmount of Rs.100 for 1 year when compounded half yearly.
= Rs. [100X(1+3/100)²]
= Rs.106.09.
∴ Effective Rate = (106.09-100)%
= 6.09%.
31. | | Mr. Ashok invested money in two schemes A and B offering compound interest @ 8% per annum and @ 9% per annum respectively. If the total amount of interest accrued through two schemes together in two years was Rs. 4818.30 and the total amount invested was Rs. 27000.What was the amount invested in scheme A ? | | (a)12,000 | | (b)13,500 | | (c)15,000 | | (d)CBD |
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Answer is: ALet the investment in scheme A be Rs. X.
Then, investment in scheme B = Rs. (27000- X).
∴[X x {(1+8/100)² - 1}+(27000 - X){(1 + 9/100)²-1}] = 4818.30
⇔ (X x 104/625) + 1881(27000 - X)/10000 = 481830/100
⇔1664X + 1881(27000 - X) = 48183000
⇔(1881 - 1664X) = 50787000 - 48183000
⇔217X = 2604000
⇔X = 12000.
32. | | If the true discount on sum due 2 years hence at 14% per annum be Rs. 168, the sum due is: | | (a)Rs. 768 | | (b)Rs. 968 | | (c)Rs. 1960 | | (d)Rs. 2400 |
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Answer is: AP.W. = (100 x T.D.)/R x T = (100 x 168)/(14 x 2) = 600.
Sum = Rs.(P.W. + T. D.) = Rs. (600 + 168) = Rs. 768
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