Question

12. You buy a $280,000 home. You place 14% down and borrow the rest at 7.2% interest compounded monthly. A. If you get a 30-year mortgage, what is the monthly payment? Be sure to show your work including the formula in the 4.6 lecture notes. Only solutions using formulas from the 4.6 lecture notes will receive credit.B. What is the total interest (finance charge) for the 30 year loan? Show your work.C. If you decide to pay $2400 instead. How many payments does it take to pay off the loan? Does this save you money compared to the 30 year mortgage? If so by how much. Be sure to show all your work.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

total price = $280000

rate = 7.2%

time = 30 years

Step 02:

interest compounded monthly

14% down = $280000 * 0.14 = $39200

P = $280000 - $39200 = $240800

A = P (1 + r/n) ^ nt

A = $240800 (1 + 0.072/12) ^ 12*30

`A\text{ = \$240800 (1}.006)^(360)`

A = $2074564.24 ==> total amount

I = $2074564.24 / (12*30) = $5762.68 ===> mensual amount

Step 03:

Mensual amount = $2400

$2074564.24 / $2400 = 864.4

865 payments

The answer is:

A. $5762.68

B. $2074564.24

C. 865 payments