Question : The simple interest accrued on a certain principal is Rs. 1200 in 3 years at 8% per annum. What would be the compound interest (compounding annually) accrued on twice that principal at 10% per annum in 2 years?
Option 1: Rs. 1,050
Option 2: Rs. 2,150
Option 3: Rs. 2,100
Option 4: Rs. 1,100
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Correct Answer: Rs. 2,100
Solution :
Let the principal be Rs. $x$.
Time = 3 years
Rate = 8% per annum
Simple interest after T years = $\frac{\text{Principal × Rate × Time}}{100}$
$⇒1200 = \frac{x \times 8 \times 3}{100}$
$\therefore x = 5000$
Now Principal, $P$ = Rs. 5000 × 2 = Rs. 10,000
Rate, $R$ = 10%
Time, $n$ = 2 years
$\therefore$ Compound Interest = $P[(1+\frac{R}{100})^{n}-1]$ = $[10000(1+\frac{10}{100})^{2}-1]$ = Rs. 2,100
Hence, the correct answer is Rs. 2,100.
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