Question

You can buy a car that is advertised for $24,600 on the following terms: (a) pay $24,600 and receive a $4,600 rebate from the manufacturer; (b) pay $410 a month for 5 years for total payments of $24,600, implying zero percent financing.

a. Calculate the present value of the payments for option (a) if the interest rate is 1.25% per month.

b. Calculate the present value of the payments for option (b) if the interest rate is 1.25% per month. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. Which is the better deal? Option a or Option b

Answer 1

a. Calculate the present value of the payments for option (a) if the interest rate is 1.25% per month.

Present value of the payments for option (a) = Price of car – rebate

Where,

Price of car = $24,600

Rebate = $4,600

Therefore

Present value of the payments for option (a) = $24,600 - $4,600

= $20,000

b. Calculate the present value of the payments for option (b) if the interest rate is 1.25% per month.

We can use following Present Value of an Annuity formula to calculate the present value of the payments

PV of the payments for option (b) = PMT * [1-(1+i) ^-n)]/i

Where,

Present value of the payments for option (b) (PV) =?

Monthly payment PMT =$410 per month

Number of payments n = 5 years *12 months = 60

Monthly interest rate i=1.25% per month or 0.0125

Therefore,

PV of the payments for option (b) = $410 * [1- (1+0.0125) ^-60]/0.0125

PV of the payments for option (b) = $17,234.18

Present Value of the payments for option (b) is $17,234.18

c. Which is the better deal? Option a or Option b

Option (b) is better deal as the present value of payments ($17,234.18) is less than Present value of the payments for option (a); where PV of option (a) is $20,000.