Question

You will want to buy a car for $23,000 plus 13% tax or $25,990. You are required to pay a down payment for $6k but need to finance the remaining amount. The company helps finance at 2.49% APR, and since you want to pay on a monthly basis, the company will compound this rate monthly. Calculate the monthly loan payments if the loan is amortized over 60 months.

Answer 1

Given

Car cost( Including Tax)= $ 25990

Down payment = $ 6000

APR = 2.49% Compounded Monthly

Interest rate per month = 2.49% /12 = 0.2075%

Time Period = 60 Months

Loan amount = Car cost - Down payment

= $ 25990-$ 6000

= $ 19990

Weknow that

Present value of the Future payment is equal to the loan amount.

Computation of Monthly installlment amount

We know that PV of Ordinary Annuity = C [ { 1-( 1+i)^-n } /i]

Here C = Cash flow per period

I = Interest rate per period

n = No.of payments

PV of Future payment s = C [ { 1- ( 1+0.002075)^-60}/0.002075]

$ 19990= C [ { 1-1.002075)^-60} /0.002075]

$ 19990= C [ { 1-0.883052} /0.002075]

$ 19990= C [ 0.116948/0.002075]

$ 19990= C [ 56.36041]

$ 19990/56.36041= C

C = $ 354.6816

Hence the Monthly loan payment is $ 354.6816

If you are having any doubts,please post a comment.

Thank you.please rate it.