SSC GD 2024 PYQ — Question 58

The correct answer is option 1 i.e. 20 percent.

A = $P \left(1 + \frac{r}{100n}\right)^{nt}$

( A ) is the amount after interest (Principal + Interest),

( P ) is the principal amount = 1000

( r ) is the annual rate of interest (in percentage),

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

( t ) is the number of years = 2years

Compound interest ( CI = 464.1)

The interest is compounded half-yearly, so ( n = 2 ).

A = P + CI = 1000 + 464.1 = 1464.1

⇒ 1464.1 = $\left(1 + \frac{r}{200}\right)^4$

 

⇒ $(1 + \frac{r}{200}) = (1.4641)^{1/4}$

⇒ 1 + $\frac{r}{200}$ = 1.1000

⇒ $\frac{r}{200} = 0.1000$

⇒ r = 0.1000 × 200 = 20

The rate of interest per annum is 20%.