How would you solve this math equation?

Question

this is really confusing to me.

Ms.Martin was researching the costs of financing $125,000 for a home. She found that the monthly payment for a 6.875% loan for 30 years would be $821.16 per month. She found that the monthly payment for a 6.875% loan for 20 years would be $959.77 per month.

1. Write and solve an equation to find the amount of interest she would pay altogether for the 30-year loan.
2. Write and solve an equation to find the amount of interest she would pay altogether for the 20-year loan.
3. For which loan would she pay less interest? How much would she save with that loan?
4. A loan officer tells Ms. Marin that her payment should be no more than 25% of her gross monthly income (income before taxes). How much must Ms. Martin gross yearly salary be in order to borrow $125,000 for each loan?

Answer 1

1. The amount of interest paid is total payments minus the initial value of the loan. This in the first case (30 years), the interest paid is
360*821.16 - 125,000 = 170,617.60

2. Fot a 20 year loan, the interest paid is
(240)*959.77-125,000 = 105,344.80

3. Compare the results of 1 and 2.

4. She must earn (before taxes) four times the payment. Compute this for each loan type.