On January 1, 2003 Mike took out a 30-year mortgage loan in the amount of 200,000 at an annual nominal interest rate of 6% compounded monthly. The loan was to be repaid by level end-of-month payments with the first payment on January 31, 2003. Mike repaid an extra 10,000 in addition to the regular monthly payment on each December 31 in the years 2003 through 2007.

Determine the date on which Mike will make his last payment (which is a drop payment).

• July 31, 2013
• November 30, 2020
• December 31, 2020
• December 31, 2021
• January 31, 2022

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

Solution: C

The monthly payment is [math] 200,000/a_{\overline{360}|0.05} = 1199.10[/math]. Using the equivalent annual effective rate of 6.17%, the present value (at time 0) of the five extra payments is 41,929.54 which reduces the original loan amount to 200,000 – 41,929.54 = 158,070.46. The number of months required is the solution to

[[math]]158, 070.46 = 1199.10 a_{\overline{n}|0.05}[[/math]]

Using calculator, n = 215.78 months are needed to pay off this amount. So there are 215 full payments plus one fractional payment at the end of the 216th month, which is December 31, 2020.

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