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
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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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