Question

You and your spouse have found your dream home. The selling price is $220,000; you will put $50,000 down and obtain a 30-year fixed-rate mortgage at 7.5%

Your banker suggests that, rather than obtaining a 30-year mortgage and paying it off early, you should simply obtain a 15-year loan for the same amount. The rate on this loan is 6.75%. By how much will your monthly payment increase/decrease for the 15-year loan than the regular payment on the 30-year loan?  

a. decrease; $211.57  

b. decrease; $154.72  

c. increase; $ 89.26  

d. increase; $494.59

e. increase; $315.69

Answer 1

Step 1) Calculate the monthly payment for 30 year mortgage:

We are given the following information:

Payment	PMT	To be calculated
Rate of interest	r	7.50%
Number of years	n	30.00
Monthly compounding	frequency	12.00
Loan amount	PV	220000-50000 = 170000.00

We need to solve the following equation to arrive at the required PMT

So the monthly payment is $1188.66

Step 2) Calculate the payment for the 15 year loan

We are given the following information:

Payment	PMT	To be calculated
Rate of interest	r	6.75%
Number of years	n	15.00
Monthly Compounding	frequency	12.00
Loan amount	PV	170000.00

We need to solve the following equation to arrive at the required PMT

So the monthly payment is $1504.35

Step 3) Find the difference of the two payments:

1504.35-1188.66 = 315.68

So the PMT will increase by 315.68 as suggested by option e