Question

You have just taken out a $24,000 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.)

a. When you make your first payment, $ ______ will go toward the principal of the loan and

$______ will go toward the interest.

Answer #1

**Monthly Loan
Payment**

Loan Amount (P) = $32,000

Monthly Interest Rate (n) = 0.333333% [4% / 12 Months]

Number of months (n) = 60 Months [5 Years x 12 months]

Monthly Loan Payment = [P x {r
(1+r)^{n}} ] / [( 1+r)^{n} – 1]

= [$24,000 x {0.00333333 x (1 +
0.00333333)^{60}}] / [(1 + 0.00333333)^{60} –
1]

= [$24,000 x {0.00333333 x 1.220997}] / [1.220997 – 1]

= [$24,000 x 0.0040699] / 0.220997

= $97.68 / 0.220997

= $442.00 per month

“Monthly Loan Payment = $442.00 per month”

Interest Portion of the first month payment = Beginning Loan amount balance x Monthly Interest Rate

= $24,000 x 0.00333333

= $80.00

Towards the principal of the loan = Monthly Payment – First month interest

= $442.00 - $82

= $362.00

**“Therefore, when you make
your first payment, $362.00 will go toward the principal of the
loan and $80.00 will go toward the interest”.**

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