Question

Maria is debating between two different mortgages for $155,000. She found a 20-year fixed rate loan at 7.35% and 15-year fixed rate loan at the same rate. How much more interest will she pay for the 20-year loan versus the 15-year loan?

Answer 1

Here is a present value equation which is a geometric sequence
 i = monthly int rate
v = 1/(1+i)
20 yr loan (240 months)


155,000 = P(v + v^2 + ...v^240)

15 yr loan (180 months)

155,000 = P(v + v^2+ ...v^180)

Use formula for sum of geometric series:

Sn = v + v^2 + ...vn = v(1−vn) / 1−v


Now you can find the monthly payments for each loan.
Multiply the payment by length of loan to get total payment, subtract loan amount to get total interest paid.

The answer would be $40,013.40.