A loan of 50,000 id based on an annual effective interest rate of 6%. You are given:

1. The loan is to be repaid with quarterly payments of 2125 and a final drop payment.
2. The first payment is due 1.5 years after the loan is taken out.

Calculate the number of payments of 2125 to be made.

• 28
• 29
• 30
• 31
• 32

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

Solution: D

[[math]] \begin{aligned} & 1.06=\left[1+\frac{i^{(4)}}{4}\right]^4 \\ & \frac{i^{(4)}}{4}=0.014674 \\ & 50,000(1.014674)^5=2,125 a_{\overline{n}|} \\ & n=31.86 \end{aligned} [[/math]]

There will be 31 payments of 2125 .

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