Question : If a sum of Rs. 12,500 is invested for 1 year at 12% per annum interest is compounded semi-annually, then the interest earned is:
Option 1: Rs. 1,505
Option 2: Rs. 1,535
Option 3: Rs. 1,545
Option 4: Rs. 1,550
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Correct Answer: Rs. 1,545
Solution :
Given:
Principal = Rs. 12,500
Rate of Interest = 12%
Time = 1 year
Formula used:
Amount = $P(1+\frac{\frac{R}{2}}{100})^{2n}$ where n is the time in years and $R$ is rate of interest per annum when compounded half-yearly.
CI = $P(1+\frac{\frac{R}{2}}{100})^{2n} - P$
$\therefore n = 1$ and $\frac{R}{2}$ = $\frac{12}{2}=6\%$ half-yearly
⇒ CI = $12500(1+\frac{6}{100})^{2} – 12500$
⇒ CI = $12500(1.06)^{2} – 12500$
⇒ CI = 14045 – 12500
⇒ CI = Rs. 1,545
Hence, the correct answer is Rs 1,545.
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