Question

You purchase a car worth $25077 and make a down payment of $3560. You intend to repay the balance of the car with month end car payments of $336 for 5 years and a final "buyout" at the end of 5 years. Money can earn 4,04% compounded semi-annually. What is the value of the final buyout? Answer:

Answer 1

value of buyout is $4185.74

Explanation:

given data

car worth = $25077

down payment = $3560

monthly payment = $336 = 336 × 6 = $2016 per semi annually

time = 5 year = 10 half yearly

rate = 4.04 %

to find out

value of final buyout

solution

we know here loan amount will be 25077 - 3560 = $21517

and we find present value first by formula that is

present value =
`(amount(1+r)^t - 1)/(r (1+r)^t)`

put here t = 10 and r =
`(4.04)/(200)`

so

present value =
`(2016(1+(4.04)/(200))^10 - 1)/(r (1+(4.04)/(200))^10)`

present value = 18089.96

so

loan unpaid amount is here

loan unpaid amount = 21517 - 18089.96

loan unpaid amount = $3427.04

so

now we calculate value of buyout

that is express as

amount = principal ×
`(1+r)^(t)`

amount = 3427.04 ×
`(1+(4.04)/(200))^(10)`

amount = 4185.74

so value of buyout is $4185.74