IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Term structure of interest rates
The annual effective spot rates are 4.0% for 1 year and 5.0% for 2 years. What is the price of a 2-year zero-coupon bond with a face value of Rs 100,000, to the nearest rupee?
The price is Rs 90,703. A 2-year zero-coupon bond is discounted at the 2-year spot rate of 5% effective for two years, so 100,000 divided by 1.1025 gives 90,703. The 1-year rate does not apply to this cash flow.
- ARs 90,703Correct
- BRs 92,456
- CRs 96,154
- DRs 95,238
- Rs 82,270
Explanation
Price = 100,000/(1.05)^2 = 100,000/1.1025 = 90,703. Using the 1-year rate 4% for two years gives 92,456, which is wrong because it ignores the 2-year spot rate.
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