Revision as of 15:03, 19 November 2023 by Admin (Created page with "A loan of 20,000 is to be repaid with ten increasing installments payable at the end of each year. Each installment will be 10% greater than the preceding installment. The annual effective interest rate on the loan is 9%. Calculate the amount of principal in the second installment. <ul class="mw-excansopts"><li>292</li><li>527</li><li>975</li><li>1435</li><li>1774</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 19'23
Exercise
A loan of 20,000 is to be repaid with ten increasing installments payable at the end of each year. Each installment will be 10% greater than the preceding installment. The annual effective interest rate on the loan is 9%.
Calculate the amount of principal in the second installment.
- 292
- 527
- 975
- 1435
- 1774
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: B
[[math]]
\begin{aligned}
R_1= & \frac{20000}{\frac{1-\left(\frac{1.1}{1.09}\right)^{10}}{0.09-0.1}}=\frac{20000}{9.562} \\
= & 2091.61
\end{aligned}
[[/math]]
The fourth payment is [math]2091.61(1.1)=2300.71[/math]
The principal outstanding before the fourth payment is
[[math]]
2300.71 \frac{1-\left(\frac{1.1}{1.09}\right)^9}{0.09-0.1}=19708.94
[[/math]]
Interest in the fourth payment is [math]=19708.94(0.09)=1773.80[/math] [math]X=[/math] Principal repaid [math]=2300.71-1773.80=526.91[/math]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.