IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods
The one-year spot rate is 3% effective. The one-year forward rate for the year from time 1 to time 2 is 7% effective. What is the two-year annual effective spot rate, to two decimal places?
The two-year spot rate is 4.98%. Compound the one-year spot and the forward rate to get 1.03 × 1.07 = 1.1021, then take the square root to annualise, giving 1.04981. Averaging 3% and 7% to get 5.00% ignores compounding.
- A4.50%
- B4.98%Correct
- C5.00%
- D5.50%
- 10.21%
Explanation
(1+s2)^2 = 1.03 × 1.07 = 1.1021, so 1+s2 = 1.04981 and s2 = 4.98%. The 5.00% option takes the simple average of 3% and 7%, ignoring compounding. The 10.21% option is the total two-year growth, not annualised.
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