Question

You have just taken out a $17,000 car loan with a 8% 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

Loan amount (PV) = $17000

No of monthly installments (N) = 60

APR (I) = 8% p.a = 0.6667% p.a.

Therefore Installment amount (PMT) = ??

Using financial calculator or PMT function in excel

Therefore Installment amount (PMT) = $ 344.6987029

Interest for 1st month = principal balance outstanding at beginning of month 1 x APR x 1/12

Interest for 1st month = 17000 x 8% /12 = $ 113.3333333

Therefore principal component in 1st month installment = Installment amount - Interest amount

Principal component in 1st month installment = 344.6987029 - 113.3333333 = $ 231.3653696

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