Sunday

November 29, 2015
Posted by **Alexis** on Wednesday, December 5, 2007 at 4:26pm.

Then I have to modify question B under the assumption that they DID pay an extra $75 in principal each month during the same 10 years but still have 6.75 closing costs. How much equity does the couple have then?

- math -
**Damon**, Wednesday, December 5, 2007 at 6:01pmBefore they made their first payment, the house is presumably still worth 129,000 and they borrowed 107,000 so their initial equity is what they paid in cash:

129,000 - 107,000 = 22,000 initial equity

Now after ten years they will owe less principal on their loan. I will assume that you have mortgage tables that give the payment, interest amount, principal amount, and remaining principal for each month of the thirty years.

From the tables you find that after ten years your remaining principal debt will be 92,352

So now, after ten years you owe 92,352 to the bank.

But you can sell the house for (1-.0675)*165,000 = 153,863 in cash after closing costs (I am rounding to the nearest dollar)

So now their equity is 153,863 - 92,352 = 61,511

(almost triple their initial 22,000 initial investment) This is the power of leveraging as long as prices go up (as they no longer are).

Now if they pay an additional 75 per month, that will increase their equity by decreasing the principal they owe the bank. One way to do this is to figure out how much $75 monthly payments add up to at 7.25% for ten years by tables or with annuity computation:

monthly interest rate,

r= .0725/12=.00604167

number of payments in ten years,

n = 12*10 = 120

accumulation = $75* [ (1+r)^n -1]/r

accumulation = 75* [2.060232-1]/r

= 75 * 175.49

= 13,161 principal accumulated by depositing 75/month for ten years

so at the end of ten years you really owe: 92,352 - 13,161 = 79,191

You got the same cash, 153,863 after closing costa but now owe the bank only 79,190

so your equity now is

153, 863 - 79,190 = 74,672