In: Accounting
saved $3000 for a down payment on a car. the largest monthly payment you can afford is $400. The loan will be at 8%APR based on end of month payments.
a) What is the most expensive car you can afford if you finance for 48 months?
b) What is the most expensive car financing 60 months?
Solution: | ||||
a. | The most expensive car you can afford if you finance for 48 months =$19,384.77 | |||
Working Notes: | ||||
The most expensive car you can afford if you finance for 48 months = is the present value of all the payments made in 48 months and down payments | ||||
1st Present value of all the payment made during 48 month. | ||||
present value of annuity = Px (1-1 /(1 + i)^n)/ i | ||||
P=monthly payment = $400 | ||||
i= interest rate per period = 8%/12 | ||||
n= no. Of period = 48 | ||||
PV of annuity= ?? | ||||
present value of annuity = Px[ 1-1 /(1 + i)^n]/ i | ||||
=400 X (1-1/(1+(8%/12))^48)/(8%/12) | ||||
=$16,384.76518 | ||||
=$16,384.77 | ||||
The most expensive car you can afford if you finance for 48 months = is the present value of all the payments made in 48 months and down payments | ||||
=$16,384.77 + $3000 | ||||
=$19,384.77 | ||||
b. | The most expensive car you can afford if you finance for 60 months =$22,727.37 | |||
Working Notes: | ||||
The most expensive car you can afford if you finance for 60 months = is the present value of all the payments made in 60 months and down payments | ||||
1st Present value of all the payment made during 60 month. | ||||
present value of annuity = Px (1-1 /(1 + i)^n)/ i | ||||
P=monthly payment = $400 | ||||
i= interest rate per period = 8%/12 | ||||
n= no. Of period = 60 | ||||
PV of annuity= ?? | ||||
present value of annuity = Px[ 1-1 /(1 + i)^n]/ i | ||||
=400 X (1-1/(1+(8%/12))^60)/(8%/12) | ||||
=$19,727.373333 | ||||
=$19,727.37 | ||||
The most expensive car you can afford if you finance for 60 months = is the present value of all the payments made in 60 months and down payments | ||||
=$19,727.37 + $3000 | ||||
=$22,727.37 | ||||
Please feel free to ask if anything about above solution in comment section of the question. |