Question : Rachit invests Rs. 12,000 for a 2-year period at a certain rate of simple interest per annum. Prasad invests Rs. 12,000 for a 2-year period at the same rate of interest per annum as Rachit, but in Prasad's case, the interest is compounded annually. Find the rate of interest per annum if Prasad receives Rs. 172.80 more as interest than Rachit at the end of the 2-year period.
Option 1: 10%
Option 2: 8%
Option 3: 12%
Option 4: 5%
Correct Answer: 12%
Solution :
Given,
Rachit invests Rs. 12,000 for 2 years at a certain rate of simple interest
Prasad invests Rs. 12,000 for 2 years at the same interest rate per annum as Rachit, but in Prasad's case, the interest is compounded annually.
Difference in interest is Rs. 172.8
Difference between Compound Interest and Simple Interest for 2 years = $P(\frac{R}{100})^2$ where $P$ is the principal, $R$ is the rate of interest
Let the rate of interest be R
$172.8 = 12000 × (\frac{R}{100})^2$
⇒ $172.8 = 12000 × \frac{R^2}{10000}$
⇒ $172.8 = 1.2 × R^2$
⇒ $144 = R^2$
⇒ $R = 12$
Hence, the correct answer is 12%.
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