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
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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