Question

You are looking at a home that will cost $250,000 and are trying to decide between two different fixed-rate mortgages. The closing costs are the same on each loan and the lender does not charge points for either loan. One mortgage would be a fifteen (15) year mortgage and have a stated annual interest rate of 4.50%. This mortgage would require you to put down 20% of the cost of the home. The other mortgage would be a thirty (30) year mortgage, and the stated annual interest rate would be 5.25%, and would require you to put down only 10% of the cost of the home.

a. What is the monthly mortgage payment on each mortgage?

b. How much of the 30-year mortgage would be left to pay when the 15-year mortgage would mature?

c. What is the incremental annualized interest-rate cost of the 30-year mortgage?

Answer 1

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

(a) EMI for 15 year mortgage

house cost= 250,000

down payment= 20% i.e $50,000

loan amount= 200,000

tenure =15 years or 180 months

ROI=4.5%

EMI= $1,529

EMI for 30 year mortgage

house cost= 250,000

down payment= 10% i.e $25,000

loan amount= 225,000

tenure =30 years or 360 months

ROI=5.25%

EMI= $1,242

(B) Amount remaining to be paid when the 15 year mortgage would mature

=1,242*180months= $223,560

(c) incremental annualized interest cost of 30 year mortgage

Interest cost for 30 year mortgage= appx $ 222,285

Interest cost for 15 year mortgage= appx $75,398

=(222,285-75,398)*100/(250,000*30)= 1.96%