SSC GD 2024 PYQ — Question 53

The correct answer is option 3 i.e. 3.6 percent.

A = $P \left(1 + \frac{r}{n}\right)^{nt}$

A is the total amount after interest (25766.4),

P is the principal (24000),

r is the annual interest rate,

n is the number of times interest is compounded per year (2 for half-yearly compounding),

t is the number of years (2).

⇒ $25766.4 = 24000 \left(1 + \frac{r}{2}\right)^{2 \times 2}$

⇒ $25766.4 = 24000 \left(1 + \frac{r}{2}\right)^4$

⇒ $\frac{25766.4}{24000} = \left(1 + \frac{r}{2}\right)^4$

⇒ $1.0736 = \left(1 + \frac{r}{2}\right)^4$

⇒ $\sqrt[4]{1.0736} = 1 + \frac{r}{2}$

⇒ $1.018 = 1 + \frac{r}{2}$

⇒ 1.018 = $\frac{r}{2}$

⇒ r = 0.036 ×  100 = 3.6%