A loan of Rs. 2,00,000 at 12% per annum compounded quarterly is to be repaid in 8 equal quarterly instalments, each paid at the end of a quarter, by the reducing balance method. Each instalment is (Given \((1.03)^{-8} = 0.7894\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 28,490.03
By the reducing balance method, the instalment E for a loan P repaid in n payments at rate i per period is
\( \displaystyle E = \frac{P\,i}{1 - (1+i)^{-n}} \)
The payments are quarterly, so the rate per quarter is used:
\( \displaystyle i = \frac{0.12}{4} = 0.03,\quad n = 8 \)
\( \displaystyle E = \frac{200000 \times 0.03}{1 - 0.7894} \)
\( \displaystyle E = \frac{6000}{0.2106} = 28490.03 \)
Why the other options are incorrect
Option (1) Rs. 25,000 — Incorrect. This is 2,00,000 ÷ 8, which leaves out the interest.
Option (3) Rs. 31,000 — Incorrect. This is the flat rate instalment, (2,00,000 + 48,000) ÷ 8.
Option (4) Rs. 27,660.22 — Incorrect. This is 28,490.03 ÷ 1.03, the instalment if each were paid at the beginning of the quarter.