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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Financial instruments and insurance contracts as cashflow models

Rs 1,000 is paid at the end of each year for 3 years, and the effective annual rate is 8%. Using standard notation, which expression gives the accumulated value at the end of year 3, and what is it to two decimal places?

The accumulated value of a three-year immediate annuity is 1000 times s three, where s three equals (1.08 cubed minus 1) divided by 0.08, which is 3.2464. The result is Rs 3,246.40.

  1. A1000 s(3 at 8%) = Rs 3,246.40Correct
  2. B1000 a(3 at 8%) = Rs 2,577.10
  3. C1000 s(3 at 8%) = Rs 3,506.11
  4. D1000 ä(3 at 8%) = Rs 2,783.26
  5. 1000 s(3 at 8%) = Rs 3,000.00

Explanation

s(3) = (1.08^3 - 1)/0.08 = (1.259712 - 1)/0.08 = 3.2464. Accumulated value = Rs 3,246.40. Option a(3) is the present value, not accumulation; 3,506.11 is the annuity-due accumulation.

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