IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods
The annual effective spot rates are 5% for a one-year term and 6% for a two-year term. What is the one-year forward rate for the year starting at time 1, to two decimal places?
The forward rate is 7.01%. Accumulating at the two-year spot rate must equal accumulating at the one-year spot and then the forward rate, so f = 1.06² / 1.05 − 1 = 7.01%. The linear shortcut of 7.00% ignores compounding.
- A5.50%
- B6.00%
- C7.00%
- D7.01%Correct
- 8.02%
Explanation
No-arbitrage requires (1.06)^2 = 1.05 × (1 + f). So 1 + f = 1.1236 / 1.05 = 1.07010, giving f = 7.01%. The 7.00% option comes from the linear approximation 2×6% − 5%, which ignores compounding.
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