Question

Rhonda wants to take out a 30-year, $280,000 loan with a 4.4% APR. She is considering purchasing 2 points, which will decrease her APR by 0.125% per point. Each point will cost 1% of her loan. Compare her monthly payments WITH and WITHOUT the purchase of the points. HELP!!!

Answer 1

Without Points: $1,402.13

With Points: $1,361.09

Explanation:

Answer 2

Given Information:

Loan amount = $280,000

Annual Percentage Rate = APR = 4.4% = 0.044

Number of years = 30

Required Information:

Monthly payment with points = ?

Monthly payment without points = ?

Answer:

Monthly payment with points = $1,361

Monthly payment without points = $1,402.13

Explanation:

The monthly payment can be found using,

`MP = P* (r* (1+r)^(n))/((1+r)^(n) - 1)`

P is the loan amount.

Where interest rate r is given by

`r = (APR)/(12)`

Total number of payments n are given by

`n = 30*12 = 360`

Monthly payment with points:

Rhonda is considering purchasing 2 points and each decreases APR by 0.125%

So the APR becomes

`APR = 4.4\% - 0.125(2)\\\\APR = 4.4\% - 0.25\%\\\\APR = 4.15\%`

and the corresponding interest rate r is

`r = (APR)/(12)\\\\r = (4.15\%)/(12)\\\\r = 0.3458\% \\\\r = 0.003458`

Finally, the monthly payment is

`MP =280,000* (0.003458* (1+0.003458)^(360))/((1+0.003458)^(360) - 1)\\\\MP =280,000* 0.0048608 \\\\MP = \$ 1,361`

Monthly payment without points:

Interest rate r is,

`r = (APR)/(12) \\\\r = (4.4)/(12) \\\\r = 0.3667\% \\\\r = 0.003667`

Monthly payment is,

`MP =280,000* (0.003667* (1+0.003667)^(360))/((1+0.003667)^(360) - 1)\\\\MP =280,000* 0.0050076 \\\\MP = \$ 1,402.13`

So monthly payment with points is $1,361 and monthly payment without points is $1,402.13