Single correct option
A loan of Rs 21,000 is to be repaid in two equal annual instalments, with interest at 10% per annum compounded annually. What is each instalment?
- A. Rs 11,550
- B. Rs 12,000
- C. Rs 12,100
- D. Rs 12,600
Show answer and solution
Answer: (C) Rs 12,100
The present values of the instalments must add up to the loan:
x/1.1 + x/1.21 = 21,000.
Put both over 1.21: x(1.1 + 1)/1.21 = 21,000, so 2.1x = 25,410 and x = 12,100.
Check: after one year the debt is 23,100. Paying 12,100 leaves 11,000, which grows to 12,100 by the end of year 2 and is cleared by the second instalment. ✓
Why others fail: 11,550 = 21,000 × 1.1/2 ignores interest in the second year.
x/1.1 + x/1.21 = 21,000.
Put both over 1.21: x(1.1 + 1)/1.21 = 21,000, so 2.1x = 25,410 and x = 12,100.
Check: after one year the debt is 23,100. Paying 12,100 leaves 11,000, which grows to 12,100 by the end of year 2 and is cleared by the second instalment. ✓
Why others fail: 11,550 = 21,000 × 1.1/2 ignores interest in the second year.
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