I am offering a lot of points. In order to get them you must have very part of t

Question

I am offering a lot of points. In order to get them you must have very part of this question. All work must be shown on all three parts.

2. You have decided to purchase a new Toyota Prius Hybrid and have a choice of methods to pay for it. The sticker price for the car is $27,000. (Show your work.)

a. What will be your monthly payments be if you pay the car off in 4 years (48 monthly payments) at 4%?

b. The dealer will offer a $2,000 rebate (price reduction), but you will have to pay 7% interest for 4 years. Will you choose this offer or what was offered in (a)?

c. Finally, if you can only afford $200/month in payments for the car, how many months will it take for you to pay the car off at 5%?

Explanation / Answer

2)

a)

let x be the monthly payment

present value of loan = 27000

PV = x * [1 - (1+i)^-n]/i

x * [1 -(1+0.04/12)^-48]/0.04/12 = 27000

x = 609.64................ans

b)

PV = 25000

x * [1 -(1+0.07/12)^-48]/0.07/12 = 25000

x = 598.66

hence we choose this offer since its monthly payment is less

c)

let t be the no of months it takes to pay

200 * [1 - (1+0.05/12)^-t]/0.05/12 = 27000

7/16 = (241/240)^-t

t = 198.82 months

t = 199 months ......................ans

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