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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value

Rs 1,000 is invested at the end of each of the next 3 years in an account that credits interest at a nominal rate of 8% per annum convertible quarterly. What is the accumulated value of these deposits at the end of year 3?

The accumulated value is Rs 3,254.09. A nominal 8% convertible quarterly is 2% per quarter, an effective annual rate of 8.2432%. Accumulating three annual deposits at this rate gives 1,000 times s3, which is 3,254.09. Treating 8% as the effective rate understates the value.

  1. ARs 3,000.00
  2. BRs 3,254.09Correct
  3. CRs 3,060.40
  4. DRs 3,246.40
  5. Rs 3,522.33

Explanation

The effective annual rate is 1.02^4 - 1 = 8.2432%. The accumulated value is 1,000 x (1.02^12 - 1)/0.082432 = 1,000 x 0.268242/0.082432 = 3,254.09. Using 8% effective gives 3,246.40, and using 2% per year gives 3,060.40, both of which ignore the correct conversion of the rate. Rs 3,522.33 treats the deposits as made at the start of each year.

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