Question

In how may years will a sum of Rs. 320 amount to Rs. 405 if interest is compounded at 12.5% per annum?

• A. 2(1/2) years
• B. 2 years
• C. 1 year
• D. 1(1/2) years

Answer 1

Answer:

B. 2 years

Solution:

Given:

Sum = Rs. 320

Amount = Rs. 405

Rate of interest = 12.5%

Formula Used:

If a^m = aⁿ, then

m = n

$Amount = P\times{(1+\frac{r}{100})^t}$

⇒ P → Principal, r% → Rate of interest per annum, t → Time period

Calculations:

Let the time period be t years.

$Amount = P\times{(1+\frac{r}{100})^t}$

⇒ $405 = 320\times{(1+\frac{12.5}{100})^t}$

⇒ $\frac{405}{320} = (\frac{9}{8})^t$

⇒ $\frac{81}{64}=(\frac{9}{8})^2=(\frac{9}{8})^t$

⇒ t = 2 years

∴ The time in which a sum of Rs. 320 amount to Rs. 405 is 2 years.