Question : The compound interest on Rs. 12000 for 9 months at 20% per annum, interest being compounded quarterly is:
Option 1: Rs. 1,750
Option 2: Rs. 2,089.70
Option 3: Rs. 1,891.50
Option 4: Rs. 2,136.40
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Correct Answer: Rs. 1,891.50
Solution :
Given: The Principal amount is Rs. 12,000, the annual interest rate (in decimal form) is 20% per annum, the number of times interest is compounded per year is 4 and the time the money is invested for (in years) is 9 months, which is $\frac{9}{12}=\frac{3}{4}$ years.
We know the formula, $A = P × (1 + \frac{r}{n})^{n × t}$.
Substitute the given values in the above formula, we get,
$A = 12000 × (1 + \frac{0.20}{4})^{4 × \frac{3}{4}}$
⇒ $A = 12000 × (1 + 0.05)^{3}$
⇒ $A = 12000 × (1.05)^{3}$
⇒ $A = 13891.5$
Compound interest is given as A – P.
= 13891.50 – 12000 = Rs. 1,891.50
Hence, the correct answer is Rs. 1,891.50.
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