A loan of ₹2,550 is to be paid back in two equal half-yearly instalments. How much is each instalment if the interest is compounded half-yearly at 8% p.a.?

Given:

Principal (P) = ₹2,550

Rate (r) = 8% p.a. compounded half-yearly

Number of instalments (n) = 2

Formula used:

Instalment amount (A) = \(\dfrac{P \times (1 + \frac{r}{2 \times 100})^n}{\dfrac{(1 + \frac{r}{2 \times 100})^n - 1}{\frac{r}{2 \times 100}}}\)

Calculations:

Rate per half year = \(\frac{8}{2} = 4%\)

⇒ Instalment amount (A) = \(\dfrac{2550 \times (1 + \frac{4}{100})^2}{\dfrac{(1 + \frac{4}{100})^2 - 1}{\frac{4}{100}}}\)

⇒ Instalment amount (A) = \(\dfrac{2550 \times (1.04)^2}{\dfrac{(1.04)^2 - 1}{0.04}}\)

⇒ Instalment amount (A) = \(\dfrac{2550 \times 1.0816}{\dfrac{1.0816 - 1}{0.04}}\)

⇒ Instalment amount (A) = \(\dfrac{2757.08}{\dfrac{0.0816}{0.04}}\)

⇒ Instalment amount (A) = \(\dfrac{2757.08}{2.04}\)

⇒ Instalment amount (A) = ₹1,352

∴ The correct answer is option 2.