Question : In what time will INR 3,20,000 amount to INR 4,05,000 if compounded at 12.5% per annum?
Option 1: 1 year
Option 2: 2 years
Option 3: 3 years
Option 4: 4 years
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Correct Answer: 2 years
Solution :
Rate, $R$ = 12.5%
Principal, $P$ = INR 3,20,000
Amount = INR 4,05,000
Let $n$ be the time.
When compounded annually, total amount after $n$ years = $P[(1+\frac{R}{100})^{n}$
$⇒405000=320000[(1+\frac{12.5}{100})^{n}$
$⇒\frac{405000}{320000} = (1+\frac{1}{8})^n$
$⇒\frac{81}{64} = (\frac{9}{8})^n$
$⇒(\frac{9}{8})^2 = (\frac{9}{8})^n$
$⇒n = 2$ years
Hence, the correct answer is 2 years.
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