Question

If a sum of money doubles itself in 10 years at compound interest, then in how many years will it become 16 times of itself at the same rate?

• A. 10
• B. 20
• C. 30
• D. 40

Answer 1

Answer:

D. 40

a sum of money doubles itself in 10 years at compound interest.

In 10 years P becomes 2P

$P(1+\frac{R}{100})^{10}=2P$

$(1+\frac{R}{100})^{10}=2$ ---------------------(1)

In how many years it becomes 16 times of itself

$P(1+\frac{R}{100})^t=16P$

$(1+\frac{R}{100})^t=16$

$(1+\frac{R}{100})^t=2^4$ ------------------------(2)

By Comparing (1) & (2).,

$((1+\frac{R}{100})^{10})^4=(1+\frac{R}{100})^t$

$t=40 years$