IAI Actuarial Core Principles · Business Economics · Role of money and interest rates in the economy
Under the pure expectations theory, the one-year spot rate is 6% per annum and the two-year spot rate is 7% per annum (annual compounding). What is the implied one-year forward rate one year from now, to the nearest 0.01%?
The implied forward rate is 8.01%. It is found by dividing the two-year accumulation factor, 1.07 squared or 1.1449, by the one-year factor of 1.06, which gives 1.0801. The linear shortcut of 8.00% ignores compounding.
- A7.00%
- B8.00%
- C8.01%Correct
- D6.50%
- 7.50%
Explanation
(1.07)^2 = 1.1449. Dividing by 1.06 gives 1.08009, so the forward rate is 8.01%. Simply doubling 7% and subtracting 6% gives 8.00%, which ignores compounding and is slightly wrong.
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