A customer has the option to either buy a car for cash for 15,000 or lease it with a down payment of 1000 and monthly payments of X payable at the end of each month for three years. Under the purchase option, the car has a value to the customer of 8000 at the end of three years. At the end of the three-year lease, the car is returned and has no value to the customer.

The customer is indifferent to the options at an annual nominal interest rate of 12% convertible monthly.

Calculate X.

• 259
• 269
• 279
• 289
• 299

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

Solution: C

[[math]]\begin{aligned} & 15,000-\frac{8000}{1.01^{36}}=1000+X a_{\overline{36} \mid 0.01} \\ & 8408.60=X a_{\overline{36} \mid 0.01} \\ & 8408.60=X(30.10751) \\ & X=279.29\end{aligned}[[/math]]

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