Question

Jordan has decided to purchase a $17,500 car and would like to finance it for five years. Her bank has offered her a standard 6.9% APR, while the dealership has offered her a special 4.9% APR. How much money will she save each month by choosing financing through the dealership

Answer 1

Jordan will save $16.25 each month by choosing financing through the dealership.

Explanation:

The EMI formula is :

`(p* r*(1+r)^(n))/((1+r)^(n)-1)`

Case 1:

p = 17500

r =
`6.9/12/100=0.00575`

n =
`5*12=60`

Putting the values in formula;

`(17500*0.00575*(1+0.00575)^(60))/((1+0.00575)^(60)-1)`

=>
`(17500*0.00575*(1.00575)^(60))/((1.00575)^(60)-1)`

EMI = $345.70

Case 2:

p = 17500

r =
`4.9/12/100=0.004083`

n =
`5*12=60`

Putting the values in formula;

`(17500*0.004083*(1+0.004083)^(60))/((1+0.004083)^(60)-1)`

=>
`(17500*0.004083*(1.004083)^(60))/((1.004083)^(60)-1)`

EMI = $329.45

So, difference per month in payments will be :

`345.70-329.45=16.25` dollars

Hence, Jordan will save $16.25 each month by choosing financing through the dealership.