Question

A person purchased a ​$219 comma 867 home 10 years ago by paying 10​% down and signing a​ 30-year mortgage at 8.7​% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 15​-year mortgage at 5.4 % compounded monthly. How much interest will refinancing​ save? Money​ Saved: ​$ nothing ​(Round to the nearest cent as​ needed.)

NOTE: PLEASE WRITE NEATLY AND LABEL THE ANSWERS!!!! EXP: How much interest will financing save? Answer:

Answer 1

Loan amount = 219867 - 0.1 * 219867 = 197880.30

original loan term = 30 * 12 = 360 months

i = 8.7% / 12 = 0.725% per month

Original monthly payment = 197880.30 * (A/P, 0.725%,360)

= 197880.30 * 0.00725 * ((1 + 0.00725)^360)/((1 + 0.00725)^360-1)

= 197880.30 * 0.00725 * ((1.00725)^360)/((1.00725)^360-1)

= 197880.30 * 0.007831

= 1549.66

Loan payments after 10 yrs = 20 * 12 = 240 months

Loan principal amount due = 1549.66 * (P/A, 0.725%,240)

= 1549.66 * ((1 + 0.00725)^240-1)/(0.00725 * (1 + 0.00725)^240)

= 1549.66 * ((1.00725)^240-1)/(0.00725 * (1.00725)^240)

= 1549.66 * 113.568877

= 175993.61

New interest rate = 5.4% / 12 = 0.45%

New loan term = 15 * 12= 180 months

New monhtly payment = 175993.61 * (A/P, 0.45%,180)

= 175993.61 * 0.0045 * ((1 + 0.0045)^180)/((1 + 0.0045)^180-1)

= 175993.61 * 0.0045 * ((1.0045)^180)/((1.0045)^180-1)

= 175993.61 * 0.008118

= 1428.69

Total interest payment without refinance = 1549.66 * 360 - 197880.30 = 359997.30

Total interest payment with refinance = 1549.66 * 120 + 1428.69 * 180 - 197880.30 = 245243.10

Total interest amount saved = 359997.30 - 245243.10 = 114754.20