Question : A certain sum compounded annually after four years becomes INR 15,000 and after six years becomes INR 25,350. What is the rate of interest per annum?
Option 1: 35%
Option 2: 30%
Option 3: 40%
Option 4: 25%
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Correct Answer: 30%
Solution :
Given: A certain sum compounded annually after four years becomes INR 15,000 and after six years becomes INR 25,350.
Use the formula, $CI=P(1+\frac{R}{100})^T$ where $A$, $P$, $R$, and $T$ are the compounded amount, principal, rate, and time.
Let the principal be INR $P$.
⇒ $15000=P(1+\frac{R}{100})^4$ --------------(1)
⇒ $25350=P(1+\frac{R}{100})^6$ --------------(2)
Dividing equation (2) by equation (1),
$\frac{P(1+\frac{R}{100})^6}{P(1+\frac{R}{100})^4}=\frac{25350}{15000}$
⇒ $(1+\frac{R}{100})^2=\frac{169}{100}$
⇒ $(1+\frac{R}{100})^2=(\frac{13}{10})^2$
⇒ $1+\frac{R}{100}=\frac{13}{10}$
⇒ $\frac{R}{100}=\frac{3}{10}$
⇒ $R=30$%
Hence, the correct answer is 30%.
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