Question

1. Comparing a 15 year and 30 year mortgage. Suppose you decide to purchase a house and determine you need $250000 loan. You research loan rates and see that you can get either a 15 year loan for 2.75% or a 30 year loan for 4.5%. Determine

   1. The monthly payment on each loan

   2. The total amount of interest paid on each loan if you pay off the loan as scheduled.

   3. Compare the costs of the two loans.

   4. How does the term of each loan change if you pay an extra $100 per month?

Answer 1

1.
15 year monthly payment=250000*(2.75%/12)/(1-1/(1+2.75%/12)^(12*15))=1696.554

2.
30 year monthly payment=250000*(4.5%/12)/(1-1/(1+4.5%/12)^(12*30))=1266.71327

3.
15 year total interest=250000*(2.75%/12)/(1-1/(1+2.75%/12)^(12*15))*12*15-250000=55379.7368417

4.
30 year total interest=250000*(4.5%/12)/(1-1/(1+4.5%/12)^(12*30))*12*30-250000= 206016.778843

5.
Total cost is higher for 30 year loan

6.
15 year loan=NPER(2.75%/12,-1696.554-100,250000)=167.774148
Term changes by 12 months

7.
30 year loan=NPER(2.75%/12,-1266.71327-100,250000)=237.3639875
Term changes by 122 months