Current loan rates are based on the following term structure of interest rates:

Investment Length (years)	Spot Rate
1	5.00%
2	5.25%
3	5.75%
4	6.25%
5	7.25%

A loan of 6000 is to be repaid with a single payment of principal plus interest at the end of five years. The borrower has two choices:

1. a 5-year loan.
2. a 3-year loan to be repaid with a single payment of principal plus interest by taking out a 2-year loan at the beginning of year 4.

Calculate the annual effective interest rate on the 2-year loan such that the borrower is indifferent between the two choices.

• 6.25%
• 7.25%
• 8.26%
• 9.54%
• 11.00%

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: D

[[math]] \begin{aligned} & 1.0725^5=1.0575^3(1+f)^2 \\ & f=0.0954 \end{aligned} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.