Compound Interest
- Vijay obtains a loan of 64000 against his fixed deposits. If the rate of interest be 2.5 paise per rupee per annum. Calculate the compound interest payable after 3 years?
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P = Rs. 64000
r = 2.5 paise per rupee per annum (given)
= 0.025 rupee per rupee per annum
= 0.025 x 100 rupee per hundred rupee per annum
= 0.025 x 100 per cent per annum
= 2.5 per cent per annum
t = 3 years
C.I. = 6400[(1 + 2.5/100)3 - 1]Correct Option: A
P = Rs. 64000
r = 2.5 paise per rupee per annum (given)
= 0.025 rupee per rupee per annum
= 0.025 x 100 rupee per hundred rupee per annum
= 0.025 x 100 per cent per annum
= 2.5 per cent per annum
t = 3 years
C.I. = 6400[(1 + 2.5/100)3 - 1]
= 64000[(1.025)3 - 1]
= 64000[1.0769 - 1]
= 64000 x 0.0769
= 4921.6
= Rs. 4921
∴ The compound interest payable is Rs. 4921.
- The cash price of a refrigerator is Rs. 7044. A customer paid Rs. 2000 in case and promised to pay the remaining money in 3 yearly equal instalments at the rate of 5% per annum compound interest. What is the value of each instalment ?
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Remaining money = 7044 - 2000 = Rs. 5044
If each installment is of Rs. P
When the amount is Rs. P at the end of first, second and third year at the rate of 5% then principal will be - P/(1 + 5/100), P/(1 +5/100)2 and P/(1 +5/100)3
∴ P/(1 +5/100) + P/(1 + 5/100)2 + P/(1 +5/100)3 = 5044Correct Option: D
Remaining money = 7044 - 2000 = Rs. 5044
If each installment is of Rs. P
When the amount is Rs. P at the end of first, second and third year at the rate of 5% then principal will be - P/(1 + 5/100), P/(1 +5/100)2 and P/(1 +5/100)3
∴ P/(1 +5/100) + P/(1 + 5/100)2 + P/(1 +5/100)3 = 5044
⇒ P(20/21) + P(20/21)2 + P(20/21)3 = 5044
⇒ P(20/21) { 1 +(20/21) + (20/21)2} = 5044
⇒ P(20/21) {1 +20/21 +400/441} = 5044
⇒ P(20/21) {441 + 420 + 400/441} =5044
⇒ P(20/21) (1261/441) =5044
∴ P = (5044 x 21 x 441)/ (20 x 1261) = Rs. 1852.20
- The difference between the simple and the compound interest compounded every six months at the rate of 10 percent per annum at the end of two years is Rs. 124.05. What is the sum ?
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Let the sum be Rs. P, then
∵ [ P(1 +5/100)4 - P] - [(P x 10 x 2)/100 ] = 124.05Correct Option: D
Let the sum be Rs. P, then
∵ [ P(1 +5/100)4 - P] - [(P x 10 x 2)/100 ] = 124.05
Solving the above equation,we get P = Rs. 8000.
- A person invested a certain amount at simple interest at the rate of 6 percent annum earning Rs. 900 as an interest at the end of three years. Had the interest been compounded every year. How much more interest would he have earned on the same amount with the same interest after three years ?
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Certain sum for the person = (900 x 100)/(6 x 3) =Rs. 5000
∴ Interest on Rs. 5000 by C.I. = 5000(1 +6/100)3 - 5000 = Rs. 955.08Correct Option: C
Certain sum for the person = (900 x 100)/(6 x 3) =Rs. 5000
∴ Interest on Rs. 5000 by C.I. = 5000(1 +6/100)3 - 5000 = Rs. 955.08
∴ More interest =Rs. (955.08 - 900) = Rs. 55.08
- If a sum of money placed at compound interest becomes 3 times of itself in 3 years. In how many years will it be 9 times at the same rate of interest ?
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Let the principle be P then amount be 3P
∵ 3P =P(1 + r/100)3
⇒ 3 = (1 + r/100)3Correct Option: A
Let the principle be P then amount be 3P
∵ 3P =P(1 + r/100)3
⇒ 3 = (1 + r/100)3
On squaring on both the sides,
⇒ (3)2 = {(1 + r/100)3}2
∴ 9 = (1 + r/100)6
Hence,it will become 9 times in 6 years.
