A car dealership offers a 120-month loan for a blue car costing 30,000, with an annual nominal interest rate of 9% compounded monthly and level end-of-month payments. The dealership also offers a loan for a red car costing 33,000, with the same interest rate and end-of-month payments as for the loan for the blue car.

Calculate the number of months needed to pay off the loan for the red car

• 132
• 135
• 138
• 140
• 141

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

Solution: E

[[math]] \begin{aligned} & 30,000=P a_{\overline{120} \mid 0.0075} \\ & P=380.03 \\ & 33,000=380.03 a_{\overline{n} |0.0075} \\ & n=141 \end{aligned} [[/math]]

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