Question

What will be the Interest rate when the Principal is ₹5000 , time is 1 year and CI is ₹788.125 and the interest is compounded half-yearly?

• A. 5%
• B. 15%
• C. 10%
• D. 8%

Answer 1

The correct option is C 10%

Let the interest rate be r%.
A = P($1+\frac{r}{2\times 100}{)}^{n\times 2}$
= 5000($1+\frac{r}{200}{)}^{\frac{2}{2}\times 2}$
= 5000($1+\frac{r}{200}{)}^2$
CI = A - P
512.5 = A - 5000
A = 5000 + 512.5 = 5512.5
$\Rightarrow$ 5000($1+\frac{r}{200}{)}^2$ = 5512.5
$\Rightarrow$ $(200+r{)}^2$ = $\frac{5512.5}{5000}\times {200}^2$
$\Rightarrow$ $(200+r{)}^2$ = $\frac{1102500}{25}$ = 44100
Taking square root on both sides :
200 + r = 210
$\Rightarrow$ r = 10%.