Question

You have a 30 year $150,000 loan at 7% interest, monthly payments. Fifteen years later, you have the chance to refinance with a 15 year mortgage at 6%. However, the fees charged to make this happen are $2500. What is the return on the $2500 "investment" if you expect to remain in the home for the next 15 years? The answer is 28.89% but im not sure how they got that.

Answer 1

Using calculator:
Step 1: Original Monthly Payment
N=12*30
PV=-150000
I/Y=7%/12
FV=0
CPT PMT=997.953742768775

Step 2: Loan Outstanding
PMT=997.953742768775
PV=-150000
FV=0
I/Y=7%/12
N=12*15
CPT FV=111028.299301527

Step 3: New Monthly Payment
PV=-111028.299301527
I/Y=6%/12
N=12*15
FV=0
CPT PMT=936.919884722007

Step 4: Return on Investment
FV=0
N=12*15
PV=-2500
PMT=997.953742768775-936.919884722007=61.03385805
CPT I/Y=2.407%
Hence, return=2.407%*12=28.89%

ALTERNATIVELY Use the below formula in excel:
=RATE(15*12,PMT(7%/12,12*30,-150000)-PMT(6%/12,12*15,FV(7%/12,12*15,-PMT(7%/12,12*30,-150000),150000)),-2500,0)*12
=28.89%