Ann got a 30 year Fully Amortizing FRM for $1,000,000 at an annual interest rate of 7% compounded monthly, with monthly payments. After 5 years of payments, Ann can refinance the balance into a 25 year Fully Amortizing FRM at an annual interest rate of 6% compounded monthly, with monthly payments. Refinancing will cost Ann 1 point and $1, 500 in closing costs.If Ann refinances into this loan and makes payments for 25 years, what will be her annualized IRR from refinancing?

Based on the information given what will be her annualized IRR from refinancing is 64.799%.

First step is to calculate the PMT

PMT=PV× rate/[1-(1+rate)^time

PMT=$1,000,000×0.07/12÷[1-(1+0.07/12)^30×12

PMT=$1,000,000×0.07/12÷[1-(1+0.07/12)^360

PMT=$1,000,000×0.005833333÷[1-(1+0.005833333)^360

PMT=$5,833.333÷[1-(1.005833333)^360

PMT=$6,653.02

Second step is to calculate the present value (PV) after 5 years

PV=PMT×[1-(1+rate)^time/rate

PV=$6,653.02×1-(1+0.07/12)^25×12÷0.07/12

PV=$6,653.02×1-(1+0.07/12)^300÷0.07/12

PV=$6,653.02×1-(1+0.005833333)^300÷0.005833333

PV=$6,653.02×1-(1.005833333)^300÷0.005833333

PV=$941,315.20

Third step is to compute PMT for refinancing  when rate is 6%

PMT=PV× rate/[1-(+rate)^time

PMT=$941,315.20×0.06/12÷[1-(1+0.06/12)^360

PMT=$941,315.20×0.005÷[1-(1+0.005)^360

PMT=$4,706.576÷[1-(1.005)^360

PMT=$6,063.72

Third step is to calculate the monthly savings

Monthly savings=$6,653.02-$6,063.72

Monthly savings=$589.30

Fourth step is to calculate the Cost of refinancing

Cost of refinancing=1%×$941,315.20+$1,500

Cost of refinancing=$9,413.152+$1,500

Cost of refinancing=$10,913.152

Fifth step is to calculate the IRR

PMT savings=Cost of refinancing ×IRR÷[1-(1+IRR)^time

$589.30=$10,913.152×IRR÷[1(1+IRR)^300

Monthly IRR=5.3999%

Annualized IRR=5.3999%×12 months

Annualized IRR=64.799%

Inconclusion what will be her annualized IRR from refinancing is 64.799%.

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