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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Time Value of Money

Vikram invests Rs 10,000 at the end of each year for 3 years in a scheme earning 10% per annum compounded annually. Another Rs 10,000 is also invested at the start of the first year in a separate identical scheme with the same rate, but he is asked only about the first scheme. What is the future value of the annuity of Rs 10,000 (end-of-year payments) at the end of year 3?

The future value is Rs 33,100. With payments at each year end, the first grows for two years to 12,100, the second for one year to 11,000, and the last stays at 10,000. Adding them gives Rs 33,100. The annuity-due value would be higher.

  1. ARs 33,100Correct
  2. BRs 36,410
  3. CRs 30,000
  4. DRs 32,100

Explanation

FV of ordinary annuity = 10,000 x [(1.1)^3 - 1]/0.1 = 10,000 x 3.31 = Rs 33,100. Check: 12,100 + 11,000 + 10,000 = 33,100. Rs 36,410 is the annuity-due value (payments at start of year), and Rs 30,000 ignores interest.

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