Question : Rs. 6000 is lent at the rate of 20% per annum on compound interest (compounded half yearly). What will be the compound interest of 18 months?
Option 1: Rs. 1825
Option 2: Rs. 1986
Option 3: Rs. 1876
Option 4: Rs. 2036
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Correct Answer: Rs. 1986
Solution :
Principal, $P$ = Rs. 6000
Time, $t$ = 18 months = 1.5 years
Rate, $R$ = 20% per annum
Amount = $P(1+\frac{R}{100})^{nt}$, where $n$ is the number of times the interest is compounded per year
= $6000(1+\frac{\frac{20}{2}}{100})^{2 \times 1.5}$
= $6000 \times 1.10^3$
= Rs. 7986
Compound Interest earned = Rs. 7986 – Rs. 6000 = Rs. 1986
Hence, the correct answer is Rs. 1986.
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