Turner buys a new car and finances it with a loan of 22,000. He will make n monthly payments of 450.30 starting in one month. He will make one larger payment in n+1 months to pay off the loan. Payments are calculated using an annual nominal interest rate of 8.4%, convertible monthly. Immediately after the 18th payment he refinances the loan to pay off the remaining balance with 24 monthly payments starting one month later. This refinanced loan uses an annual nominal interest rate of 4.8%, convertible monthly.

Calculate the amount of the new monthly payment.

• 668
• 693
• 702
• 715
• 742

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

Solution: D

[[math]] \begin{array}{l l}{{O B_{18}=22.000(1.007)^{18}-450.30S_{\overline{{{18}}}|0.007}=16.337.10}}\\ {{16.337.10=P a_{\overline{{{24}}}|_{0.004}}}}&{{}}\\ {{P=715.27}}&{{}}&{{}}\end{array} [[/math]]

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