Question : There is a 40% increase in the amount in 10 years at simple interest. What will be the compound interest on Rs. 30,000 after 3 years at the same rate?
Option 1: Rs. 3,745.92
Option 2: Rs. 7,491.84
Option 3: Rs. 9,364.80
Option 4: Rs. 5,618.88
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Correct Answer: Rs. 3,745.92
Solution :
Given: Simple interest on amount $P$ after 10 years = 40% of $P$
Term for Simple Interest, $n_1$ = 10 years
Sum for compound interest, $P$ = Rs. 30,000
Term for compound interest, $n_2$ = 3 years
Simple interest after $n_1 $ years = $\frac{Pn_1R}{100}$
40% of $P = \frac{P×10×R}{100}$
⇒ $R$ = 4%
So, Rate, $R$, for compound interest = 4%
When compounded annually, compound interest after $n_2$ years = $P[(1+\frac{R}{100})^{n_2}-1]$
= $30000[(1+\frac{4}{100})^{3}–1]$
= Rs. 3,745.92
Hence, the correct answer is Rs. 3,745.92.
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