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

Answer:

The correct answer is -

monthly payment = 521.99

total pain intrest = 4319.14

Step-by-step 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, $\frac{ar}{[1-(1+r)^{-60}}$ = 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  $\frac{ar}{[1-(1+r)^{-60}}$

= 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