Single correct option
A loan of Rs 33,100 is to be repaid in three equal annual instalments, the first due one year after the loan is taken, at 10% per annum compound interest. What is the value of each instalment?
- A. Rs 11,033
- B. Rs 12,100
- C. Rs 13,310
- D. Rs 14,641
Show answer and solution
Answer: (C) Rs 13,310
The present values of the three instalments must add up to the loan:
x/1.1 + x/1.21 + x/1.331 = 33,100.
Multiply through by 1.331: x(1.21 + 1.1 + 1) = 33,100 × 1.331 → 3.31x = 44,056.1 → x = Rs 13,310.
Check: 13310/1.1 = 12100, 13310/1.21 = 11000, 13310/1.331 = 10000; total 33,100. ✓
Rs 11,033 is just 33,100/3, which ignores interest. Rs 14,641 is 10,000 × 1.1⁴.
x/1.1 + x/1.21 + x/1.331 = 33,100.
Multiply through by 1.331: x(1.21 + 1.1 + 1) = 33,100 × 1.331 → 3.31x = 44,056.1 → x = Rs 13,310.
Check: 13310/1.1 = 12100, 13310/1.21 = 11000, 13310/1.331 = 10000; total 33,100. ✓
Rs 11,033 is just 33,100/3, which ignores interest. Rs 14,641 is 10,000 × 1.1⁴.
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