Question

You want to buy a car that’s currently priced at $25,795. The price of the car in one year will be $23,610 since it will be last year’s model. You currently don’t have anything in your bank account. Consequently, if you buy the car today you will borrow $25,795 from your parents who will charge you 3.76% APR compounded monthly. You will repay the entire loan balance in one year if you decide to buy the car today. How much will you save (viewed as of one year from now) if you wait to buy the car?

Answer 1

APR = 3.76%

n = 12 months

EAR = [1 + (APR/n)]^n - 1

= [1 + (3.76%/12)]^12 - 1

= [1.003133333333]^12 - 1

= 1.03825475 - 1

= 0.03825475

= 3.83%

Car Price today = $25,795

Interest to be paid for 1 year = $25,795 * 3.83% = $987.9485 = $987.95

Total amount paid if car purchased today = $25,795 + $987.95 = $26,782.95

Car price in one year = $23,610

Amount saved if you wait and buy car = Total amount paid if car purchased today - Car price in 1 year

= $26,782.95 - $23,610

= $3,172.95

Therefore, total amount saved if you wait and buy car is $3,172.95