Question

Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.

To buy a car, you borrow $28,000 with a term of five years at an APR of 5%. What is your monthly payment? (Round your answer to the nearest cent.)
$


How much total interest is paid? (Round your answer to the nearest cent.)
$

Answer 1

9514 1404 393

Answer:

• monthly payment: $528.39
• interest paid: $3,703.40

Step-by-step explanation:

The monthly payment is given by the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where the annual interest rate is r for t years on loan value P.

Filling in the given information, we find the monthly payment to be ...

  A = $28000(0.05/12)/(1 -(1 +0.05/12)^(-12·5)) ≈ $528.39

The monthly payment is $528.39.

__

The total amount repaid is ...

  ($528.39/mo)(60 mo) = $31,703.40

The interest paid is the difference between this and the loan amount:

  interest paid = $31,703.40 -28,000 = $3,703.40

The total interest paid is $3,703.40.