Seth, Janice, and Lori each borrow 5000 for five years at an annual nominal interest rate of 12%, compounded semi-annually. Seth has interest accumulated over the five years and pays all the interest and principal in a lump sum at the end of five years. Janice pays interest at the end of every six-month period as it accrues and the principal at the end of five years. Lori repays her loan with 10 level payments at the end of every six-month period.

Calculate the total amount of interest paid on all three loans.

• 8718
• 8728
• 8738
• 8748
• 8758

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

Solution: D

The given information yields the following amounts of interest paid:

Seth = 5000 ((1+0.12/2)¹⁰-1)= 8954.24- 5000 = 3954.24

Janice = 5000(0.06)(10) = 3000.00

Lori = [math]P(10)[/math] - 5000 = 1793.40 where [math]P = \frac{5000}{a_{\overline{10}|6\%}}[/math] = 679.35

The sum is 8747.64.

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