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

Expert Answer

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


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


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


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

Answer: (b)

The customer should choose PlanA, paying $5,000 cash immediately.