A purchase of 5020 is paid off with a loan at an annual effective interest rate of 6.25%. Payments are made at the end of each year until the loan is paid off. Each payment is 360 except for a final balloon payment, which is less than 720.

Calculate the amount of the balloon payment.

• 611
• 630
• 649
• 667
• 685

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

Solution: C

[[math]] \begin{aligned} & 5020=360 a_{\overline{n}|0.0625} \\ & n=33.85 \\ & \text { Use } n=33 \\ & 5020=360 a_{\overline{33} \mid 0.0625}+X v^{33} \\ & 5020=4980.95+X v^{33} \\ & 39.05=X v^{33} \\ & X=288.75 \\ & B=360+288.75=648.75\end{aligned} [[/math]]

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