Question

Noel and Herman are now trying to decide between a 48​-month and a 60​-month car loan. If the loan is for ​$9782 at 5​percent, what is the difference in the monthly​ payments?

Answer 1

Loan balance = $9,782

Annual interest rate = 5%
Monthly interest rate = 5% / 12
Monthly interest rate = 0.4167%

If loan period is 48 months:

Let monthly payment be $x

$9,782 = $x/1.004167 + $x/1.004167^2 + ... + $x/1.004167^47 + $x/1.004167^48
$9,782 = $x * (1 - (1/1.004167)^48) / 0.004167
$9,782 = $x * 43.422614
$x = $225.27

Monthly payment = $225.27

If loan period is 60 months:

Let monthly payment be $x

$9,782 = $x/1.004167 + $x/1.004167^2 + ... + $x/1.004167^59 + $x/1.004167^60
$9,782 = $x * (1 - (1/1.004167)^60) / 0.004167
$9,782 = $x * 52.990192
$x = $184.60

Monthly payment = $184.60

Difference between monthly payments is $40.67 ($225.27 - $184.60)