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.)

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

fractionally backed paper money

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paper money

metallic money