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 Option b

Answer 1

Answer:

A. $20,000

B. $17,234.18

C.Option (b)

Explanation:

Obviously, the option with lower Present Value would be the best option to buy the car. The Present Value of the options can find out as following

REQUIREMENT A

Price of car = $24,600  

Rebate = $4,600

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

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

Present value of the payments for option = $20,000

REQUIREMENT B

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

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

PV 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

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

PV of the payments for option  = $17,234.18

REQUIREMENT C.

Which is the better deal?

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); $20,000.