A borrower takes out a loan to be repaid over 20 years. The first payment is 1102 payable at the end of the first month. Each subsequent monthly payment is five more than the previous month’s payment.

Calculate the accumulated value of the payments at the end of 15 years using an annual effective interest rate of 6.5%.

• 442,031
• 443,525
• 445,578
• 447,287
• 448,547

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

Solution: A

The effective monthly rate is . The accumulated value is

[[math]] \begin{align*} 1097 s_{\overline{180}|0.0052617} + 5(Is)_{\overline{180}|0.0052617} \\ 1097(298.733) + 5\frac{\ddot{s}_{\overline{180}|0.0052617}-180}{0.0052617} \\ 327, 710 = 5 \frac{300.3049 -180}{0.0052617}=442, 031 \end{align*} [[/math]]

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