IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Term structure of interest rates
Annual effective spot rates in India are: 1-year spot rate 6.00% and 2-year spot rate 7.00%. What is the one-year forward rate applying from time 1 to time 2, f(1,2)?
The forward rate from time 1 to 2 is 8.01%. It equals the ratio of the two-year accumulation factor 1.07 squared to the one-year factor 1.06, minus one. The approximation 8.00% ignores compounding and is not exact.
- A6.50%
- B7.00%
- C8.00%
- D8.01%Correct
- 7.50%
Explanation
(1+f) = (1.07)^2/1.06 = 1.1449/1.06 = 1.08009, so f = 8.01%. The simple average 6.5% ignores compounding. Choosing 8.00% results from using the approximation 2×7% − 6%, which is not exact.
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