Question

You need a loan of ​$140,000 to buy a home. Calculate your monthly payments and total closing costs for each choice below. Briefly discuss how you would decide between the two choices.
Choice​ 1: 30 ​-year fixed rate at 4 ​% with closing costs of ​$2100 and no points.
Choice​ 2: 30 ​-year fixed rate at 3.5 ​% with closing costs of ​$2100 and 4 points.

What is the monthly payment for choice​ 1? ​$______ ​(Do not round until the final answer. Then round to the nearest cent as​ needed.)
What is the monthly payment for choice​ 2? ​$______ ​(Do not round until the final answer. Then round to the nearest cent as​ needed.)
What is the total closing cost for choice​ 1? $______
What is the total closing cost for choice​ 2? ​$______

Why might choice 1 be the better​ choice?
A. The monthly payment is higher.
B. The monthly payment is lower.
C. The closing costs are lower.
D. The closing costs are higher.

Why might choice 2 be the better​ choice?
A. The closing costs are higher.
B. The closing costs are lower.
C. The monthly payment is higher.
D. The monthly payment is lower.

Answer 1

Answer:

• Monthly Payment for Choice 1=$665.16
• Monthly Payment for Choice 2=$627.10
• Total Closing Cost for Choice 1=$241557.60
• Total Closing Cost for Choice 2=$233456
• (A)Choice 1 be the better choice the monthly payment is higher.
• (D)Choice 2 be the better choice because the monthly payment is lower.

Explanation:

Amount of Loan needed = $140,000

• A point is an optional fee which helps you get a lower interest rate on your loan.
• Closing costs are the fees you pay when obtaining your loan.

Choice 1

30-year fixed rate at 4% with closing costs of $2100 and no points.

Monthly Payment

P=$140,000

Monthly Rate=4% ÷ 12=0.04 ÷ 12=0.0033

n=12 X 30 =360

$=\dfrac{Pr(1+r)^n}{(1+r)^n-1}$

$=\dfrac{140000X0.0033(1+0.0033)^{360}}{(1+0.0033)^{360}-1}\\=\dfrac{462(1.0033)^{360}}{(1.0033)^{360}-1}\\=\ 665.16$

Monthly Payment=$665.16

Total Closing Cost =(665.16 X 360)+2100=$241557.60

Choice 2

30-year fixed rate at 3.5% with closing costs of $2100 and 4 points.

Monthly Payment

P=$140,000

Monthly Rate=3.5% ÷ 12=0.035 ÷ 12=0.0029

n=12 X 30 =360

$=\dfrac{Pr(1+r)^n}{(1+r)^n-1}$

$=\dfrac{140000X0.0029(1+0.0029)^{360}}{(1+0.0029)^{360}-1}\\=\dfrac{406(1.0029)^{360}}{(1.0029)^{360}-1}\\=\ 627.10$

Monthly Payment=$627.10

Total Closing Cost =(627.10 X 360)+2100+(4% of 140000)=$233456