Mark is in the market for a used car. He has found the same sports car at two different dealerships and is now considering which dealer he should purchase the car from. Dealer 1 requires Mark to get the loan through their lending department. Dealer 1 has told Mark that because they do their own financing, they can get Mark the very best loan possible and Mark will only have to pay $291 per month for 60 months (5 years). Dealer 2 is selling the car for $12000. Dealer 2 has told Mark he can use their financing or get his own lender, so Mark talked with his bank and learned that he can get a 5 year car loan for 4.5% APR. Dealer 2 has also offered Mark a 5 year loan for 5.5%. Based on these loan options, what is Mark’s lowest monthly loan payment option?

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TomShelby TomShelby · Answer 1 · 2019-10-04T19:01:40+02:00

Answer:

the bank is the best option as it can purchase the car with monthly payment of 223.71 while the other option are payment for 291

Explanation:

option 1 291 per month

option 2

we can chose for a 4.5 loan or a 5.5 loan so we will pick the bank as it is lower and compare with the 291 of dealer 1

the loan of 12,000 at 4.5% APR

we need to calculate the PTM of an ordinary annuity of 5 years discounted at 4.5%

[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]

PV $12,000.00

time 60 (5 years x 12 months per year)

rate 0.00375 (we divide the annual rate by 12 to convert it to monthly)

[tex]12000 \div \frac{1-(1+0.00375)^{-60} }{0.00375} = C\\[/tex]

C $ 223.716