Question

You want to buy a house. You have found the house you like and have agreed to purchase the house for $300,000. You go to the bank to get a loan and have decided that a 30 year mortgage loan is the best loan duration. What do you think the interst rate will be on your loan given the following data?

"Real" interest rate given current macro econmomic conditions = 2.0%

The inflation rate forecasted for the future is = 1.5%

Unfortunately, your credit score sucks and you represent a bigger risk to the bank.

The added "risk" rate is = 6.0% (only 2% added risk rate if good credit rating)

Estimated bank mortgage rate =

Given the 30 year rate above, calculate your monthly house payment (assume monthly compounding).

Calculate your monthly house payment if you had a good credit score

What is the total difference in payments over the life of the loan btween a "good" rate and a "bad" rate?

Would the rate be higher or lower on a 15 year mortgage? Why?

Show excel formula for each and please explain each answer

Answer 1

Interest Rate
Real Interest Rate (A)	2.00%
Inflation Risk Premium (B)	1.50%
Default Premium risk ('C)	6.00%
Estimated bank Mortgage Rate (r=A+B+C)	9.50%
Principal Amount (P)	300,000.00
Number of Years (n)	30
Compunding (m)	Monthly
Monthly Payment =	(r/m(P))/(1-(1+r/m)^-n*m)
=	((0.095/12)*300000)/(1-(1+(0.095/12))^-(30*12))
=	2,522.56
Interest Rate
Real Interest Rate (A)	2.00%
Inflation Risk Premium (B)	1.50%
Default Premium risk ('C)	2.00%
Estimated bank Mortgage Rate (r=A+B+C)	5.50%
Principal Amount (P)	300,000.00
Number of Years (n)	30
Compunding (m)	Monthly
Monthly Payment =	(r/m(P))/(1-(1+r/m)^-n*m)
=	((0.055/12)*300000)/(1-(1+(0.055/12))^-(30*12))
=	1,703.37
Total payment with 9.5% interest=	2522.56*360=	908,121.60
Total payment with 5.5% interest=	1703.37*360=	613,213.20
Difference due bad rate		294,908.40

The rate of interest will be lower on a 15 year mortgage as this will reduce he risk . Shorter mortgages carry less risk as compared to long term mortgages.