A two-year loan of 100 is repaid with a payment of X at the end of the first year and 2X at the end of the second year. The annual effective interest rate charged by the lender is 8% in the first year and i in the second year. The annual effective yield rate for the lender is 10%.

Calculate i.

• 12.8%
• 12.9%
• 13.0%
• 13.1%
• 13.2%

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

Solution: E

Based on the effective yield rate, After one year, the outstanding loan balance is 100 + 8 – 39.03 = 68.97. For the balance to be zero after two years,

[[math]] 68.97(1+i)-2(39.03)=0\Rightarrow i=78.06/68.97-1=0.1318=13.29 \% [[/math]]

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