Question

You have just taken out a $19,000 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

Prepare summary of loan which is to be used in the main calculations, which is as follows:

Present value = $19,000

Rate = (4%) / 12 = 0.333%

Period (N) = 12 months x 5 year = 60 months

Calculate the amount of first Installment, which is as follows:

Installment = Loan amount x r x [(1+r) ^n] / [(1+r) ^n – 1]

Installment = 19,000 x 0.333% x [[(1+0.333%) ^ 5 x 12] / [(1+0.333%) ^ 5 x 12] – 1]]

Installment = 349.88

Calculate interest on first Installment, which is as follows:

Interest = Loan amount x r

Interest = 19,000 x 0.333%

Interest = 63.27

Calculate the amount of principal included m the rust installment, which is as follows:

Principal = Installment — Interest

Principal = $349.88 — 63.27

Principal = 286.61

Thus, when you make your First payment, $286.61 will go towards the principal of the loan and $63.27 will go towards the interest.