Question

You borrow $500,000 to purchase a house. The mortgage is a 30-year fixed rate mortgage, with monthly payments.

A. Assume that you have good credit, and can borrow money at a 3.75% annual interest rate. What will your monthly payment be?

B. Now, assume that you have lousy credit, and must pay a 6.5% annual interest rate to obtain a mortgage. What will your monthly payment be?

C. Having lousy credit can be costly. How much additional interest will you pay over the 30-year period if you have bad credit, relative to what you would pay if you have good credit? (Hint: Calculate the total interest over the 30-year period on the loan in Part A, and the total interest over the 30-year period for the loan in Part B. What is the difference between the two amounts?).

D. Is it ethical for banks to charge people with poor credit histories higher interest rates? [After all, people with lousy credit will benefit more from lower interest rates than people with good histories & high paying jobs (who could afford to pay more interest!)].

you must show supporting work, or describe the numbers you input to your calculator (i.e., enter PMT = 2000; i = 5%; n = 20. Solve for PV = ZZZ).

Answer 1

Part (A)

Monthly payment = PMT = ???

i = 3.75% / 12 = 0.003125; n = 12 x 30 = 360; PV = -500000, FV = 0

Hence, monthly payment = PMT (i, n, pV, FV) = PMT (0.003125, 360, -500000,0) = $ 2,315.58

Part (B)

Monthly payment = PMT = ???

i = 6.5% / 12 = 0.005417; n = 12 x 30 = 360; PV = -500000, FV = 0

Hence, monthly payment = PMT (i, n, pV, FV) = PMT (0.005417, 360, -500000,0) = $ 3,160.34

Part (C)

Total interest over the 30-year period on the loan in Part A = PMT in Part (A) x n - Loan amount = $2,315.58 x 360 - 500,000 = $333,608.0

And the total interest over the 30-year period for the loan in Part B =  PMT in Part (B) x n - Loan amount = $3,160.34
x 360 - 500,000 = $637,722.44

And the difference between the two amounts = $637,722.44 - $333,608.06 = $ 304,114.38 = additional interest will you pay over the 30-year period if you have bad credit, relative to what you would pay if you have good credit

Part (D)

A bank charges an interest from the borrower to compensate itself for the risk it is taking. Interest is just a compensation for parting away with your money today. A bank is therefore professionally correct to assume that the probability of default is higher in case of people with poor credit score It's therefore exposed to higher credit risk and hence it charges higher interest rate. Hence, the bank is ethically correct to charge people with poor credit histories higher interest rates.