A loan of 20,000 is to be repaid with payments at the end of each year for ten years. The first payment is X. Each subsequent payment is 6% greater than the preceding payment. The loan payments are based on an annual effective interest rate of 10%.

Calculate the loan balance immediately after the eighth payment.

• 6685
• 6937
• 7353
• 7794
• 8088

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

Solution: C

[[math]]\begin{aligned} & 20,000=X\left[\frac{1-\left(\frac{1.06}{1.10}\right)^{10}}{0.10-0.06}\right] \\ & X=2584.39 \\ & L B_8=X\left(\frac{1.06^8}{1.10}+\frac{1.06^9}{1.10^2}\right)=7353\end{aligned}[[/math]]

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