Exercise
A ten-year loan will be repaid with payments at the end of each year. Each of the first five payments is 1000 and each of the next five payments is 2000. Interest on the loan is charged at an annual effective rate of 10%.
Calculate the total interest paid in the first five payments.
- 2418
- 2646
- 2978
- 4083
- 4249
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Solution: D
The amount borrowed is [math]1000a_{\overline{5}|0.01} + 2000v^5a_{\overline{5}|0.1} = 8498.35[/math]. The outstanding balance after five years is [math]2000a_{\overline{5}|0.1} = 7581.57[/math]. The principal repaid is 8498.35 – 7581.57 = 916.78. The interest paid is 5000 – 916.78 = 4-83.22.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.