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