A loan for 10,000 is to be repaid by level annual payments at the end of each year for ten years. The annual effective interest rate for the loan is 10%, which the bank uses to compute the annual payment and the balance on the loan at the end of each year. However, for balances during each year, the bank uses an annual simple interest rate of 10%.

Calculate the balance of the loan halfway through the fourth year.

• 7434
• 7442
• 7885
• 8310
• 8319

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

Solution: E

The annual payment is

[[math]]10,000 a_{\overline{10}|0.01} = 10, 000 / 6.14457 = 1627.45[[/math]]

. The balance at time 3 is

[[math]]1627.45 a_{\overline{7}|0.01} = 1627.45(4.8684) = 7923.08.[[/math]]

.

With one-half year at simple interest, the balance at time 3.5 is 7923.08(1.05) = 8319.23.

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