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Quantitative Aptitude :: Compound Interest Problems And Answers

32. A sum of money on compound interest amounts to Rs. 8240 in 2 years and Rs. 9888 in 3 years. The rate of interest is
A. 10% B. 25%
C. 20% D. 12%
Answer & Explanation

Answer: Option C

Explanation: Let the sum be P and rate of interest be R% per annum.
Amount after 2 year = 8240
P(1+R/100)T = 8240
P(1+R/100)2 = 8240   --- ( 1)
Amount after 3 year = 9888
P(1+R/100)T = 9888
P(1+R/100)3 = 9888   --- (2)
(2) ÷ (1) => [P(1 + R/100)3]/[P(1+R/100)2 = 9888/8240
1+R100 = 9888/8240
R/100 = (9888/8240 − 1 )= 1648/8240 = 15
R = 100/5 = 20%

Solution 2
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If a certain sum of money at compound interest amounts to Rs.x in t1 years and Rs.y in t2 years, then the rate of interest per annum can be given by
R = [(y/x)1/(t2−t1) − 1] × 100%
R = [(y/x)1/(t2−t1) − 1] × 100 = [(9888/8240)1/(3−2) − 1] × 100 = [(9888/8240) − 1] × 100
= (1648/8240) × 100 = (15) × 100 = 20%
 

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