From Kaplan:
The Kaplan QuickSheet does not show the formula that the explanation provides.
This particular subject has always provided confusion.
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Investing for 4 years is equivalent to investing for 2 years today and rolling over for another 2 years at the forward rate:
1.07^4 = 1.05^2 * (1 + 2 yr forward rate)^2
A little bit of algebra will get you to the Kaplan solution.
Is the 2 year forward rate also 5%?
Nope: that’s the mystery rate you’re trying to find. For the first 2 years, funds earn 5%: it’s in years 3 and 4 where you get the 2 year forward rate. If you invest for 2 years at 5%, then reinvest for another 2 years at approximately 9%, you will end up with the same accumulated value as investing for 4 years at 7%.
Oh I have it now. My Algebra was a bit fuzzy at first.
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An approximation that provides a good check is to add all of the annual rates, rather than compounding them:
4 × 7\% ≈ 2 × 5\% + 2 ×\ _2f_2
28\% ≈ 10\% + 2 ×\ _2f_2
2 ×\ _2f_2 ≈ 18\%
_2f_2 ≈ 9\%
The correct value is 9.0381\% to four decimal places.