Revision as of 14:58, 19 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>6685</li><li>6937</li><li>7353</li><li>7794</li><li>8088</li></ul> {{soacopyright | 2023 }}")
Nov 19'23
Exercise
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.
Nov 19'23
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.