# Three Purchase Plans Are Available For A New Car.Plan A: \$5,000 Cash ImmediatelyPlan B: \$1,500 Down And 36 Monthly Payments Of

Three purchase plans are available for a new car.

Plan A: \$5,000 cash immediately

Plan B: \$1,500 down and 36 monthly payments of \$116.35

Plan C: \$1,000 down and 48 monthly payments of \$120.50

If a customer expects to keep the car five years and his cost of money is 18% compounded monthly, which payment plan should he choose?

a. Any Plan!
b. Plan A
c. Plan B
d. Plan C

This solution was written by a subject matter expert. It’s designed to help students like you learn core concepts.

Step-by-step

Step 1/1

To calculate the present value of each plan, we can use the following formula:

Present value = Future value / (1 Interest rate)^n

where:

Present value is the current worth of a future payment

Future value is the amount of money that will be received or paid in the future

Interest rate is the annual interest rate, compounded monthly

n is the number of months until the future payment

For Plan A, the present value is simply the cost of the car, \$5,000.

For Plan B, the future value is the total cost of the car, which is \$1,500 down payment 36 monthly payments of \$116.35=\$5,654.20. The present value of Plan B is:

Present value = \$5,654.20 / (1 0.18 / 12)^60 = \$3,659.61

For Plan C, the future value is \$1,000 down payment 48 monthly payments of \$120.50=\$6,540.00. The present value of Plan C is:

Present value = \$6,540.00 / (1 0.18 / 12)^60 = \$4,142.38

Explanation:

Therefore, Plan A has the lowest present value, making it the best option for the customer.