Question

You have just taken out a $ 23 comma 000 car loan with a 4 % ​APR, compounded monthly. The loan is for five years. When you make your first payment in one​ month, how much of the payment will go toward the principal of the loan and how much will go toward​ interest? ​(Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

Answer:

Interest = $75.90

Principal = $347.64

Explanation:

First find the payment that is required per month. It will be an Annuity payment as the present value of the loan is given.

The loan is for 5 years compounded monthly so period is;

= 5 years * 12 months

= 60

Interest = 4/12

Present Value of Annuity= Payment * (1 - (1 + r) ^ -n)/r

23,000 = Payment * (1 - ( 1 + 4/12%) ^ -⁶⁰)/ 4/12%

23,000 = Payment * 54.304

Payment = 23,000/54.304

= $423.54

Interest Payment is;

= 4/12% * 23,000

= $75.90

Amount going towards Principal;

= 423.54 - 75.90

= $347.64