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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time Value of Money and Annuity - Simple and Compound Interest

A firm wants to accumulate Rs 2,100 at the end of 2 years by making equal deposits at the end of each of the 2 years at 10% p.a. compound interest. What should each annual deposit be?

Each deposit should be Rs 1,000. With year-end deposits at 10% for two years, the accumulation factor is 1.10 plus 1, which is 2.10. Dividing the target Rs 2,100 by 2.10 gives Rs 1,000. Simply dividing by two would ignore interest earned.

  1. ARs 1,000Correct
  2. BRs 1,050
  3. CRs 954
  4. DRs 1,100

Explanation

Future value of an ordinary annuity of 2 payments = P x (1.10 + 1) = 2.10P. So P = 2,100 / 2.10 = Rs 1,000. Rs 1,050 ignores interest and divides by 2. Rs 954 treats it as an annuity due (2,100/2.31 is 909, not it either) and so uses the wrong factor.

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