Question : On a certain sum, simple interest at the annual rate of 12% for 6 years is Rs. 28800. What will be the compound interest on the same sum at the annual rate of 20% (compounding annually) for 2 years?
Option 1: Rs. 17600
Option 2: Rs. 19200
Option 3: Rs. 12000
Option 4: Rs. 14400
Correct Answer: Rs. 17600
Solution :
$I = \frac{PRT}{100}$
where $I$ = simple interest, $P$ = principal amount (the sum), $R$ = rate of interest, and $T$ is the time period.
Given that the simple interest $I$ is Rs. 28800, the rate of interest $R$ is 12% per annum, and the period $T$ is 6 years.
⇒ $28800 = \frac{P × 12 × 6} { 100}$
⇒ $P$ = Rs. 40000
⇒ $CI = P(1 + \frac{r}{100})^n - P$
where $CI$ = compound interest, $P$ = principal amount (the sum), $r$ = rate of interest, and $n$ = time period.
Given that the principal sum $P$ is Rs. 40000, the rate of interest $r$ is 20% per annum, and the time $n$ is 2 years.
⇒ $CI = 40000(1 + \frac{20}{100})^2 - 40000$
= $40000×(\frac{36}{25}) - 40000$
= 57600 – 40000
= Rs. 17600
Hence, the correct answer is Rs. 17600.
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