Mortgage Question Set

*For these problems we will ignore property taxes and any type of homeowner's insurance.*

Family A took out a standard 30 year fixed mortgage to pay for their \$200,000 home. They put down \$40,000 (20%) from a combination of inheritance and savings for which their terms then became: 3.35% APR, \$160,000, and a period of 30 years (or 360 monthly payments). Because Family A had a solid credit rating, they were able to obtain a lower interest rate.

1.) Considering this mortgage, what is their monthly payment?
(a) \$1,062.95
(b) \$705.14
(c) \$954.67
(d) none of the above

*Step 1: We need to calculate effective interest rate per month since 3.35% APR is for the year.

*.0335/12(months)= .00279
*multiply by 100 (.00279*100)= .2791% per month (Multiplying this by 12 will be 3.35%)

*Step 2: Now we need to calculate the number of N payment periods

*N= 12(months)*(30 years)= 360 months

*Step 3: Set up the formula and solve, which in our case, is A (payment per month)

* A= 160,000(A/P, i= .2791%, 360)
*Using Excel or a graphing calculator will result in a \$705.14 monthly payment,which is B.

Family B was approved of a \$200,000 mortgage (standard 30 year fixed), purchasing the same house price as Family A in Question 1. Since no down payment was made, terms were as follows: 7.5% APR, \$200,000, 30 years (360 payments). Family B's credit rating wasn't up to par so they couldn't obtain a lower interest rate because the bank considers them to be a higher risk.

2.) How much does Family B pay in interest over the course of the 30 year mortgage?
(a) \$50,834
(b) \$303,434.45
(c) \$60,826.34
(d) \$80,821.68

*Step 1: Let's calculate the effective interest rate per month again with the same procedure

* i =(.075/12)*100= .625% per month
*We know N is equal to 360

*Step 2: Set up the formula and solve for A
* A= 200,000(A/P, i = .625%, 360)
* A= \$1,398.43 per month

*Step 3: Calculate the future value of all loan payments made month by month, that is, the total you pay pay in principle and interest over the life of the mortgage.
*Since we will be making 360 payments, multiply 360 months by \$1,398.43 per month (Remember, interest is already included in the monthly payment we calculated)
* F= 360*1398.43 = \$503,434.45, which is the total of all payments.

*Step 4: To find the total interest paid we subtract:
*Total interest paid= (total of all payments) - (principle)
*Total interest paid = 503,434.45 - 200,000= \$303,434.45, which is B. This is what we paid on top of the principal.

3.) How much more does Family B pay in interest than Family A?
(a) \$106,374.63
(b) \$209,584.05
(c) \$157,616.23
(d) none of the above
(e) pink flamingos

*Step 1: Let's calculate the sum of all payments, principal and interest, Family A makes over the course of their mortgage
*Using our \$705.14 per month payment (From question 1) we multiply by 360 months (Remember, interest is already included in that monthly payment we calculated)
*Total of all payments= 705.14 * 360 = \$253,850.40

*Step 2: Subtract our our principal from the total payment to get our total interest paid
* Total interest paid= (total of all payments) - (principle)
*253,850.40 - 160,000 = \$93,850.40 total interest paid This is how much we pay on top of principal

*Step 3: Now we use Family B's \$303,434.45 total interest paid from Question 2 and take away Family A's total interest paid of \$93,850.40

* Interest difference is: 303,434.45 - 93,850.40 = \$209,584.05 more in interest, which is B.

All in all Family B is paying much more interest than A is by a large margin. They could've put more of their money towards retirement or for a college education, but they didn't save up any money for a down payment nor did they clean up their credit before taking on a mortgage. They will also have to pay for Private Mortgage Insurance (PMI) which protects the bank in case they don't make payments. Certain decisions can cost thousands….

4.) Why might both families choose a 30 year fixed versus a 15 year fixed mortgage?
(a) Plan to own house for a longer period of time
(b) Lower monthly payments
(c) Easier to qualify for with a higher loan amount
(d) All the above

The answer is D. The 15 year mortgage may be attractive if you plan to own the home for a short period of time and if you want to make faster payments.

page revision: 10, last edited: 19 Oct 2016 00:51