Question : Find the sum of money invested by a man in a scheme that offers compound interest(compounding annually) at a 6% rate of interest per annum if compound interest for 2 years is Rs. 618.
Option 1: Rs. 7000
Option 2: Rs. 9000
Option 3: Rs. 5000
Option 4: Rs. 4000
Correct Answer: Rs. 5000
Solution :
$\text{Total Amount}=\text{Principal}[(1+\frac{\text{Rate}}{100})^{\text{Time}}-1]$
$⇒\text{618}=\text{Principal}[(1+\frac{\text{6}}{100})^{\text{2}}-1]$
$⇒\text{618}=\text{Principal}[(\frac{\text{106}}{100})^{\text{2}}-1]$
$⇒\text{618}=\text{Principal}[(\frac{\text{11236}}{10000})-1]$
$⇒\text{618}=\text{Principal}[(\frac{\text{1236}}{10000})]$
$⇒\text{618}\times (\frac{10000}{1236})=\text{Principal}$
$\therefore\text{Principal}=5000$
Hence, the correct answer is Rs. 5000.
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