Question : If interest is compounded half-yearly, then find the compound interest on INR 8,000 at 20% p.a. for 1 year.
Option 1: INR 1,675
Option 2: INR 1,690
Option 3: INR 1,685
Option 4: INR 1,680
Correct Answer: INR 1,680
Solution : Use : Amount = P(1+ $\frac{r}{n})^{nt}$, where r = interest rate (decimal) P = Principal n = number of terms in a year t = time period According to the question Amount = P(1+ $\frac{r}{n})^{nt}$ Now, ⇒ Amount = 8000(1+ $\frac{0.20}{2})^{2 × 1}$ = 8000(1+ $0.10)^{2}$ = 8000 × 1.21 = 9680 Compound Interest = Amount − Principal = 9680 − 8000 = INR 1,680 Hence, the correct answer is INR 1680.
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