A student borrows money to pay for university tuition. He borrows 1000 at the end of each month for four years. No payments are made to repay the loan until the end of five years. The loan accumulates interest at a 6% nominal interest rate convertible monthly for the first two years and at an 8% nominal interest rate convertible monthly for the following two years.

Calculate the loan balance at the end of four years immediately following the receipt of the final 1000.

• 54,098
• 55,224
• 55,762
• 56,134
• 56,350

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

Solution: C

The accumulated value is

[[math]] 60,000=2000a_{\overline{35}|0.01}+Pv^{36}=58,817.16+0.698925P = 1000(25.4320(1.1729) + 25.9332) = 55, 762 [[/math]]

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