A 15-year loan of 60,000 is to be repaid with payments of X at the end of each month based on an annual nominal interest rate of 7.5%, convertible monthly. When the loan balance is 49,893, the loan is refinanced at an annual nominal interest rate of 6.0%, convertible monthly. Payments remain at X and are paid at the end of each month for as long as necessary, with a smaller final payment.

Calculate the total number of payments, including the smaller final payment.

• 162
• 164
• 166
• 168
• 170

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

Solution: D

Using BA II Plus:

[[math]] \begin{aligned} & 60,000=X a_{\overline{180}|0.075 / 12} \\ & X=556.21 \\ & 49,893=556.21 a_{\overline{m}|0.075 / 12} \\ & m=132 \end{aligned} [[/math]]

So, [math](180-132)=48[/math] payments have been made so far:

[[math]] \begin{aligned} & 49,893=556.21 a_{\overline{n}|{0.6 / 12}} \\ & n=119.3 \end{aligned} [[/math]]

Use 120 future payments including the smaller one. [math]48+120=168[/math].

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