Question

You plan to purchase a $390,000 house using either a 30-year mortgage obtained from your local savings bank with a rate of 8.50 percent, or a 15-year mortgage with a rate of 7.55 percent. You will make a down payment of 20 percent of the purchase price. a. Calculate the amount of interest and, separately, principal paid on each mortgage. What is the difference in interest paid? b. Calculate your monthly payments on the two mortgages. What is the difference in the monthly payment on the two mortgages? (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) a. Calculate the amount of interest and, separately, principal paid on each mortgage. What is the difference in interest paid? b. Calculate your monthly payments on the two mortgages. What is the difference in the monthly payment on the two mortgages?

a. Interest under 15-year mortgage:

Interest under 30-year mortgage:

Difference in interest paid:

b. Monthly payment under 15-year mortgage

Monthly payment under 30-year mortgage

Difference in monthly payment:

Answer 1

We solve part B first:

Mortgage 1:

Using financial calculator

Amount of loan = PV = -390000*80% =-312000

N = 30*12 = 360

I/Y = 8.5/12

Find Monthly payment = PMT = $2,399.01

Mortgage 2:

Using financial calculator

Amount of loan = PV = -390000*80% =-312000

N = 15*12 = 180

I/Y = 7.55/12

Find Monthly payment = PMT = $2,901.15

Difference = $2,901.15 - 2399.01 = $502.14

A: Interest paid on Mortgage 1= Total payment -Principal

= 2399.01*360 - 312000

=551643.6

Principal = amount of loan = 312000

Interest paid on Mortgage 2= Total payment -Principal

= 2901.15*180 - 312000

=210207

Principal = amount of loan = 312000

Difference in Interest = 551643.6 – 210207 = 341436.6