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CA Foundation · Quantitative Aptitude · Mathematics of Finance

Ramesh borrows ₹21,000 at 10% per annum compound interest and agrees to repay it in two equal instalments paid at the end of year 1 and year 2. What is the amount of each instalment?

Each instalment is ₹12,100. The present value of two equal year-end payments at 10% must equal the loan, so P × (1/1.1 + 1/1.21) = 21,000. Then P = 12,100, since 12,100/1.1 + 12,100/1.21 = 11,000 + 10,000 = 21,000.

  1. A₹10,500
  2. B₹12,600
  3. C₹11,550
  4. D₹12,100Correct

Explanation

The instalment P satisfies P/1.1 + P/1.21 = 21,000, i.e. P × (1.1 + 1)/1.21 = 21,000, so P = 21,000 × 1.21/2.1 = ₹12,100. Check: 12,100/1.1 + 12,100/1.21 = 11,000 + 10,000 = 21,000. The figure ₹12,600 comes from using simple interest on the full loan for 2 years.

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