A 25-year loan is being repaid with annual payments of 1300 at an annual effective rate of interest of 7%. The borrower pays an additional 2600 at the time of the 5th payment and wants to repay the remaining balance over 15 years.

Calculate the revised annual payment.

• 1054.58
• 1226.65
• 1300.00
• 1369.38
• 1512.12

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

Solution: B

Just prior to the extra payment at time 5, the outstanding balance is

[[math]] 1300 a_{\overline{20}|0.07}=1300(10.5940) =13, 772.20. [[/math]]

After the extra payment it is 11,172.20. Paying this off in 15 years requires annual payments of

[[math]] 11,172.20/a_{\overline{15}|0.07}=11,172.20 / 9.1079 = 1226.65. [[/math]]

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