SSC GD 2024 PYQ — Question 46

The correct answer is option 3 i.e. 81 percent.

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

(A) is the total amount after interest = 2200 + 3836.8 = 6036.8

(P) is the principal amount = 2200

(r) is the annual interest rate (in decimal form).

(n) is the number of times interest is compounded per year.

(t) is the time the money is invested for = 1.5 years

Compounding frequency (n = 2) (since interest is compounded half-yearly).

⇒ 6036.8 =$2200 \left(1 + \frac{r}{2}\right)^{2 \times 1.5}$

⇒ 6036.8 =$2200 \left(1 + \frac{r}{2}\right)^3$

⇒ $\frac{6036.8}{2200} = \left(1 + \frac{r}{2}\right)^3$

⇒ 2.745 = $\left(1 + \frac{r}{2}\right)^3$

⇒$\sqrt[3]{2.745} = 1 + \frac{r}{2}$

⇒ 1.405 = 1 + r / 2

⇒ 1.405 - 1 = r / 2

⇒ 0.405 = r / 2

⇒ r = 0.810 × 100 = 81%