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On a certain sum, the compound interest accrued in the first two years is Rs. 5520 and that in the first three years is Rs. 9576. What is the rate of interest ?
- A10 %
- B20 %
- C30 %
- D40 %
Correct answer: C
Discussion 1
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0
CCommunity
30 %
CI = P[(x)1 - 1] where x = 1 + r/100
∴ P (x² - 1) = 5520 ...... (1)
P(x3 - 1) = 9576 ...........(2)
Dividing eqn II by eqn I,
(x² + x + 1) (x - 1)/(x + 1) (x - 1) = 9576/5520 = 399/230
= 230x² - 169x - 169 = 0
= 230x² - 299x + 130x - 169 = 0
= 23x (10x - 13) + 13 (10x - 13) = 0
∴ x = 13/10 and x = -13/23 (discard-ve)
1 + r/100 = 13/10
∴ r = 30%
CI = P[(x)1 - 1] where x = 1 + r/100
∴ P (x² - 1) = 5520 ...... (1)
P(x3 - 1) = 9576 ...........(2)
Dividing eqn II by eqn I,
(x² + x + 1) (x - 1)/(x + 1) (x - 1) = 9576/5520 = 399/230
= 230x² - 169x - 169 = 0
= 230x² - 299x + 130x - 169 = 0
= 23x (10x - 13) + 13 (10x - 13) = 0
∴ x = 13/10 and x = -13/23 (discard-ve)
1 + r/100 = 13/10
∴ r = 30%