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%.  

PART A- Assume that monthly payments begin in one month. What will each payment be?

a. $ 901.52  

b. $1,188.66  

c. $1,359.74  

d. $1,563.01  

e. $1,722.80  

PART B- How much interest will you pay (in dollars) over the lifetime of the loan? (Assume you make each of the required 360 payments on time.)  

a. $235,101  

b. $245,583  

c. $257,919

d. $290,457  

e. $370,457  

PART C- What will the outstanding balance of the loan be after five years assuming you make the first 60 payments exactly on time?  

a. $ 59,321

b. $128,225

c. $147,551

d. $160,850

e. $170,000

PART D- Although you will get a 30-year mortgage, you plan to prepay the loan by making an additional payment each month along with your regular payment. How much extra must you pay each month if you wish to pay off the loan in 20 years?  

a. $ 90.56  

b. $154.88  

c. $180.85

d. $203.28  

e. $226.86  

PART E- 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

Loan Amount =Selling Price-Down payment =220000-50000=170000
Number of months =30*12 =360
Rate per month =7.5%/12
a) Monthly Payment =Loan Amount/((1-(1+r)^-n)/r) =170000/(((1-(1+7.5%/12)^-360)/(7.5%/12)) =1188.6647 or 1188.66(Option b is correct option)

b) Interest over the lifetime =Number of Months*Monthly Payment -Loan Amount =1188.6647*360-170000 =257919.29 (Option c is correct option)

c) Outstanding balance after 5 years or 60 months =PV*(1+r)^n-PMT*((1+r)^n-1)/r)
=170000*((1+7.5%/12)^60-1188.6647*(((1+7.5%/12)^60-1)/(7.5%/12)) =160849.64 or 160850(Option d is correct option)

d) Monthly Payment if number of month of 240
=Loan Amount/((1-(1+r)^-n)/r) =170000/(((1-(1+7.5%/12)^-240)/(7.5%/12)) =1369.51
Extra payment =1369.51-1188.66 =180.85(Option c is correct option)