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.)

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Business

Rex Marshall

26 February, 10:33

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.)

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Veronica Goodman · 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.