Question

nicole has the choice of taking out a 30-year loan for $165,000 at 9.1% interest, compounded monthly, or the same loan at 25 years for a higher monthly payment. how much more is the monthly payment for the 25-year loan than the monthly payment for the 30- year loan

Answer 1

The monthly payment for 25 years is $56.50 more than the monthly payment for 30 years loan.

Explanation:

The formula to be used is :

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

1st scenario:

p = 165000

n =
`30*12=360`

r =
`((9.1)/(12))/100` = 0.00758

Putting the values in the formula we get

`(165000*0.00758 * (1.00758)^(360) )/((1.00758)^(360)-1 )`

= $1339.045

2nd scenario:

p = 165000

n =
`25*12=300`

r =
`((9.1)/(12))/100` = 0.00758

Putting the values in the formula we get

`(165000*0.00758 * (1.00758)^(300) )/((1.00758)^(300)-1 )`

= $1395.540

The difference in the monthly payments are =

`1395.540-1339.045=56.495` dollars ≈ $56.50

Therefore, the monthly payment for 25 years is $56.50 more than the monthly payment for 30 years loan.