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”.