IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting
A zero-coupon bond pays Rs 1,00,000 at the end of 5 years. It is priced at Rs 74,726 today. What effective annual rate of interest does this imply, to the nearest 0.01%?
The implied effective annual rate is 6.00%. The ratio of maturity value to price is 1.3382, and this equals 1.06 raised to the fifth power, so compounding over five years at 6% reconciles the price with the payment.
- A6.00%Correct
- B5.00%
- C7.00%
- D6.50%
- 5.50%
Explanation
Need (1+i)^5 = 100000/74726 = 1.33823. 1.06^5 = 1.33823, so i = 6.00%. Simple average return 25.274%/5 = 5.05%, which is why 5.00% is wrong: it ignores compounding.
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