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