IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Key assurance and annuity contracts
An annuity pays ₹1,000 at the end of each year for 10 years, with the first payment due at time 6 (that is, deferred 5 years). At an effective annual rate of 5%, what is its present value?
The present value is ₹6,050.18. Payments run from time 6 to time 15, so the value is 1000 × v^5 × a_10, or equivalently 1000 × (a_15 - a_5), at 5% interest.
- A₹5,762.07
- B₹4,329.48
- C₹10,379.66
- D₹6,050.18Correct
- ₹6,352.69
Explanation
Payments are at times 6 to 15, so the value is 1000 × v^5 × a_10 = 1000 × 0.783526 × 7.721735 = 6,050.18. Check: a_15 - a_5 = 10.379658 - 4.329477 = 6.050181. ₹6,352.69 wrongly uses a deferment of 4 years, which would put the first payment at time 5.
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