A 15-year loan with an annual effective interest rate of 6% has payments of 400 at the end of each year. At the time of the fifth payment, the borrower pays an extra 1000 and then repays the balance over five years with a revised annual payment of X.

Calculate X.

• 264.13
• 435.38
• 461.51
• 556.46
• 698.90

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

[[math]] \begin{aligned} & O B_5=400 a_{\overline{100.06}}-1000=1944.03 \\ & 1944.03=X a_{51} 0.06 \\ & X=461.51 \end{aligned} [[/math]]

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