Question

Hello, I have tried this problem at least 10 different times now and cannot get the correct answer according to my homework website. It'd be great if someone can figure out what the answer is:

Joe Levi bought a home in Arlington, Texas, for $127,000. He put down 25% and obtained a mortgage for 30 years at 8%. What is the difference in interest cost if he had obtained a mortgage rate of 6%? (Do not round intermediate calculations. Round your answer to the nearest cent.)

Answer 1

Cost of house: $127,000

Down payment: 25% of $127,000 = $31,750

Principal financed: $127,000 - $31,750 = $95,250

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

where A = monthly payment,

P = principal borrowed

r = interest rate per period

n = number of periods

8% loan:

n = 30 * 12 = 360

r = 8/100/12 = 0.08/12

P = $95,250

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

$A = \dfrac{(0.08/12)(95250)(0.08/12 + 1)^{360}}{(0.08/12 + 1)^{360 - 1}}$

A = $698.9107566 per month

In 360 months, you pay 360 of those payments, for a total of

$251,607.87238

6% loan:

n = 30 * 12 = 360

r = 6/100/12 = 0.06/12 = 0.005

P = $95,250

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

$A = \dfrac{(0.005)(95250)(0.005 + 1)^{360}}{(0.005 + 1)^{360 - 1}}$

A = $571.07187 per month

In 360 months, you pay 360 of those payments, for a total of

$205,585.87507

Now subtract the amounts of total payments to find the difference in interest: $251,607.87238 - $205,585.87507 = $46,021.9973

Answer: $46,022.00

Answer 2

So first you’d do 25% of $127,000 which is $31,750, and subtract it from $127,000 because that’s how much Joe put down on the home. You get $95,250. Then you determine what 8% of $95,250 is ->> $7,260. He paid that for 30 years which comes to $217,800. Now you do 6% of $95,250 which is ->> $5,715. Paying that for 30 years would give you $171,450. To get the The interest for 8% would be $44,450 and the interest for 6% would be $90,800. To get the difference in interest you will now subtract $44,450 from $90,800 and you get $46,350.