You take out a car loan for 13,381 dollars. If your loan has an annual interest rate of 8.86 percent, and you will make monthly payments for 5 years, how much of your first payment will go towards principal (go towards paying down the outstanding loan balance)?

Principal paid in the first payment =$2,656.52

Explanation:

Loan Amortization: A loan repayment method structured such that a series of equal periodic installments will be paid for certain number of periods to offset both the loan principal amount and the accrued interest.  

We will use the following relationships:

Interest paid = Interest rate × loan balance

Principal paid = Monthly installment - Interest paid

Monthly installment  = Loan amount/Annuity factor

Annuity factor = (1- (1+r)^(-n))/r

r - annual interest rate

n- number of period = 12× 5 = 60

Monthly interest rate - 8.86/12 =0.738 %

Loan amount = 13,381

Annuity factor = (1 - (1.00738)^(-60) )/ 0.00738=48.336

Monthly interest payment = Loan amount/Annuity factor

                                         13,381/48.336=2,755.32

Interest due in the first month = interest rate × loan amount

                      =  0.738 %×  13,381 =98.796

Principal aid in the first year = Monthly installment - interest due 1st month

                      = 2,755.32 - 98.796 = 2,656.52

Principal paid in the first payment =$2,656.52

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