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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


Team Careers360 15th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

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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