Question

You need a loan of $160,000 to buy a home. Calculate your monthly payments and total closing costs for each choice below.

Choice 1: 30 year fixed rate at 5% with closing costs if $2300 and no points.

Choice 2: 30 year fixed rate at 4.5% with closing costs of $2300 and 5 points.

What is the monthly payment for choice one?

What is the monthly payment for choice two?

what is the total closing cost for choice one?

what is the total closing cost for choice two?

why might choice one be better?

why might choice two be better?

Answer 1

Choice 1: 30 year fixed rate at 5% with closing costs if $2300 and no points.

Choice 2: 30 year fixed rate at 4.5% with closing costs of $2300 and 5 points

1. What is the monthly payment for choice one

Loan amount = $160000

Period   t = 30y

Rate of interest r = 5% = 5/100 = 0.05

And compounding frequency is monthly so t = 30 x 12 = 360

And Rate of interest r = 0.05 / 12= 0.0041667 monthly

Now we can use the below formula to find the monthly payment (PMT)

PMT = [ p x r x (1+r)^t ] / [(1+r)^t-1]

PMT = [ 160000 x 0.0041667 x (1+0.0041667)³⁶⁰ ] / [(1+0.0041667)³⁶⁰-1]

PMT = [ 666.672 x 4.46779 ] / [4.46779 - 1]

PMT = [ 2978.5504] / [3.46779]

PMT = 858.9189 ~ 859

So the monthly payment = $859

2. What is the monthly payment for choice two

Loan amount = $160000

Period   t = 30y

Rate of interest r = 4.5% = 4.5/100 = 0.045

And compounding frequency is monthly so t = 30 x 12 = 360

And Rate of interest r = 0.045 / 12= 0.00375 monthly

Now we can use the below formula to find the monthly payment (PMT)

PMT = [ p x r x (1+r)^t ] / [(1+r)^t-1]

PMT = [ 160000 x 0.00375 x (1+0.00375)³⁶⁰ ] / [(1+0.00375)³⁶⁰-1]

PMT = [ 600 x 3.84769 ] / [3.84769 - 1]

PMT = [ 2308.614] / [2.84769]

PMT = 810.697 ~ 810.7

So the monthly payment = $810.7

3. What is the total closing cost of choice one

Form the given information closing cost for choice one is $2300

4. What is the total closing cost of choice two

Form the given information closing cost for choice two is $2300 and 5 points.

So 5 points = 5% of principal amount

                   = 160000 x 5/100

                = 8000

So total closing cost = 2300 + 8000 = $10300

5) why might choice one better?

Because of there is no points to include in the closing cost and it was very low when compare with choice two.

6. why might choice one better?

When compare two choices 2^nd choice is having less monthly payment.