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 $27,000 with a term of five years at an APR of 6%. 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

The correct answer is -

monthly payment = 521.99

total pain intrest = 4319.14

Explanation:

Given:

a or the borrowed amount = 27000

r or the interest rate = 6%

n = 5 years or 60 months

Monthly payment = ?

total intreset = ?

Formula:

The formula for the monthly payment is -

`\frac{a}{\frac{{[(1+r)^n]-1}}{[r(1+r)^n]}} = P`

or,
`(ar)/([1-(1+r)^(-60))` = P

Where, the amount of the loan = a

r = 0.005 (6% annual rate—expressed as 0.06—divided by 12 monthly payments per year)

n = 60 months

Solution:

Putting all the values in the either of the following formula will give monthly payments:

`\frac{27000}{\frac{{[(1+0.005)^(60)]-1}}{[0.005(1+0.005)^(60)]}} = P` or
`(ar)/([1-(1+r)^(-60))`

= 521.9856 or to the nearest cent 521.99.

The total intrest would be -

= (monthly payment*number of month) - amount borrowed

= 521.99*12-27000

= 31319.14-27000

= 4319.14