Question

You purchase a $225,000 town home and you pay 20% down. You obtain a 30 year fixed rate mortgage with an annual interest rate of 3.75%. After 20 years you refinance the mortgage for 10 years at a 3.25% annual interest rate. After you refinance what is the new monthly payment to the nearest dollar? 1.) 797 2.)814 3.) 932 4.)1,335 5.) 1,500

Answer 1

Step 1 - Find out the monthly loan payment of first loan
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan amount = $225000 X 80% = $180000
P = monthly loan payment = ?
r = monthly interest rate = 3.75%/12 =0.003125
n = number of monthly payments = 30 years * 12 = 360
180000 = P x {[1 - (1+0.003125)^-360]/0.003125}
180000 = P x 215.9288
P = 833.61
Monthly Loan payment = $833.61
Step 2 - Find out loan outstanding amount after 20 years
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan outstanding = ?
P = monthly loan payment = 833.61
r = monthly interest rate = 3.75%/12 =0.003125
n = number of monthly payments remaining = 10 years * 12 = 120
Present value of annuity = 833.61 x {[1 - (1+0.003125)^-120]/0.003125}
Present value of annuity = 833.61 x 99.93879
Present value of annuity = 83309.78
Loan outstanding after 20 years = $83,309.78
Step 3 - Find out the new monthly payment after refinancing the loan outstanding in step 2
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = loan outstanding = 83309.78
P = new monthly loan payment = ?
r = monthly interest rate = 3.25%/12 =0.002708
n = number of monthly payments = 10 years * 12 = 120
83309.78 = P x {[1 - (1+0.002708)^-120]/0.002708}
83309.78 = P x 102.3342
P = 814.10
The new monthly payment to the nearest dollar = $814
The answer is $814.