Question : A sum of INR 10,500 amounts to INR 13,650 in 2 years at a certain rate percent per annum simple interest. The same sum will amount to what in 1 year at the same rate if the interest is compounded half yearly (nearest to INR 1 )?
Option 1: INR 12,124
Option 2: INR 12,134
Option 3: INR 12,143
Option 4: INR 12,314
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Correct Answer: INR 12,134
Solution : Given, A sum of INR 10,500 amounts to INR 13,650 in 2 years at a certain rate percent per annum simple interest compounded half-yearly We know, Simple interest = $\frac{\text{Principal × rate × time}}{100}$ Amount = Principal(1 + $\frac{r}{100}$) t If interest is compounded half yearly then time becomes double and the rate becomes half ⇒ Simple interest = 13,650 - 10,500 ⇒ Simple interest = INR 3150 ⇒ 3150 = $\frac{10,500 × r × 2}{100}$ ⇒ 3150 = 105 × r × 2 ⇒ r = $\frac{3150}{105 × 2}$ ⇒ r = 15% Now, For compounded half-yearly Rate = $\frac{15}{2}\%$ Time = 2 years Amount = 10,500(1 + $\frac{15}{200}$) 2 = 10,500(1 + $\frac{3}{40}$) 2 = 10,500 × $\frac{43}{40} × \frac{43}{40}$ = INR 12,134 Hence, the correct answer is INR 12,134.
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