Question : A certain sum of money amounts to 3 times itself in 13 years when interest is compounded annually at a certain interest rate per annum. In how many years will the initial sum amount to 9 times itself at the same interest rate per annum, also compounded annually?
Option 1: 32 years
Option 2: 26 years
Option 3: 30 years
Option 4: 20 years
Correct Answer: 26 years
Solution :
Given: A certain sum of money amounts to 3 times itself in 13 years when interest is compounded annually at a certain interest rate per annum.
Use the formula, $A=P[1+\frac{R}{100}]^T$ where $A$, $P$, $R$ and $T$ are the amount, principal, rate, and number of years.
Let the sum be INR $P$.
According to the question,
$3P=P[1+\frac{R}{100}]^{13}$
⇒ $3=[1+\frac{R}{100}]^{13}$ ----------------(1)
On squaring both sides of the equation (1),
⇒ $3^2=([1+\frac{R}{100}]^{13})^2$
⇒ $9=[1+\frac{R}{100}]^{26}$
⇒ $9P=P[1+\frac{R}{100}]^{26}$ [Multiplying both sides by $P$]
So, the required number of years is 26.
Hence, the correct answer is 26 years.
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