Question

A friend bought a house 15 years ago, taking out a $120,000 mortgage at 6% for 30 years. How much does she still owe on the mortgage?
You can afford a $700 per month mortgage payment. You’ve found a 30 year loan at 5% interest.
a. How big of a loan can you afford?
b. How much total money will you pay the loan company?
c. How much of that money is interest?


Marie can afford a $250 per month car payment. She’s found a 5 year loan at 7% interest.
a. How expensive of a car can she afford?
b. How much total money will she pay the loan company?
c. How much of that money is interest?

Answer 1

1)  First you need to find the monthly payment.
$m = P\frac{i(1+i)^{360}}{(1+i)^{360} - 1}, P = 120,000, i = 0.005 \\ \\ m = 719.46$

Next, you need a function for balance remaining at time 't'.
$B(t) = (P-\frac{m}{i})(1+i)^t +\frac{m}{i} \\ \\ B(180) = 85,258.8$

So after 15 years, she still owes 85,258.80 on the mortgage.