A five-year interest-only loan in the amount of 10,000 has annual payments, and an annual effective interest rate i. At the end of year 5, the borrower pays off the principal along with the last interest payment.

To finance the principal payment, the borrower buys the following two zero-coupon bonds that both mature at the end of year 5.

	Time of Purchase	Par Value	Annual Effective Yield
Bond 1	End of year 3	2000	3.0%
Bond 2	End of year 4	8000	2.5%

It costs the borrower a total of 2260.19 at the end of year 3 to pay the interest due and to buy Bond 1.

Calculate i.

• 2.60%
• 3.00%
• 3.18%
• 3.75%
• 4.30%

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

Solution: D

The cost to purchase the bond at the end of year 3 is 2000 x (1.03)^-2 = 1,885.19 . Subtracting this cost from 2260.19 we get 375, the amount of interest paid which is 3.75% of 10000. Thus the interest rate is 3.75%.

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