I am answering questions concerning equity, the problem is a story problem, and it concerns a couple who bought a 129000 home, and then borrowed 107,000 at 7.25% for 30 years. A) How much equity does the couple have in their home before they make their first mortgage payment? B) How much equity would they have 10 years later if they could sell the home for 165,000? Also assume that the couple must pay 6.75% closing costs.

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?

Before 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

To find the answers to these questions, we need to understand the concept of equity and how it is calculated.

Equity is the difference between the market value of a property and the outstanding mortgage balance. It represents the ownership interest or financial stake that a homeowner has in their property.

A) To find the couple's equity in their home before making their first mortgage payment, we need to subtract the borrowed amount from the home's purchase price.

Equity = Home Purchase Price - Borrowed Amount
Equity = $129,000 - $107,000
Equity = $22,000

Therefore, before making the first mortgage payment, the couple has $22,000 in equity in their home.

B) To determine their equity 10 years later, we need to calculate the remaining mortgage balance and then subtract it from the estimated selling price of the home.

First, let's calculate the remaining mortgage balance using the loan details:

Loan Amount: $107,000
Interest Rate: 7.25%
Loan Term: 30 years

We can use a mortgage calculator or a loan amortization schedule to help us with the calculations. Let's assume we use a loan amortization schedule.

After 10 years, the remaining mortgage balance can be determined by finding the principal balance after 10 years of payments.

Next, let's calculate the closing costs, which are 6.75% of the selling price.

Closing Costs = 6.75% of Selling Price
Closing Costs = 0.0675 * $165,000
Closing Costs = $11,137.50

Finally, we can calculate the couple's equity after 10 years by subtracting the remaining mortgage balance and closing costs from the selling price.

Equity = Selling Price - Remaining Mortgage Balance - Closing Costs

Under the assumption that the couple did not make any extra principal payments during the 10-year period, the equity calculation would be:

Equity = $165,000 - Remaining Mortgage Balance - $11,137.50

Now, as per your modification in question B, if the couple did pay an extra $75 in principal each month during the same 10-year period, we need to adjust the remaining mortgage balance accordingly before calculating the equity.

To find the remaining mortgage balance with extra principal payments, we deduct the total principal payments made over 10 years from the original loan amount.

Extra principal payments over 10 years = $75 * 12 * 10 = $9,000
Remaining Mortgage Balance (with extra principal payments) = Loan Amount - Extra principal payments

Then, the new equity calculation would be:

Equity = $165,000 - Remaining Mortgage Balance (with extra principal payments) - $11,137.50

By following these steps, you can find the equity of the couple in both scenarios.