**Answer:**

Answer is explained in the explanation section below.

**Explanation:**

**Solution:**

**Note: In this question, Cash Flow table is used as well, which I have attached below. Please refer to that table as well. **

Monthly payment for the 30 year FRM loan:

PV = 1,500,000; r (monthly interest rate) = 6%/12 = 0.5%; n (number of monthly payments) = 30*12 = 360

PMT (monthly payment) =

PMT (monthly payment) = = (0.5%*1,500,000)/(1 -(1+0.5%)^-360) = 8,993.26

**Balance remaining after 8 years (if refinancing is not done): **

PMT = 8,993.26; r = 0.5%; n = 360 - (8*12) = 264

PV = PMT*(1 - (1+r)^-n)/r = 8,993.26*(1 - (1+0.5%)^-264)/0.5%

**PV = 1,316,585.31 **

**Balance remaining after 3 years (if refinancing is done):**

PMT = 8,993.26; r = 0.5%; n = 360 - (3*12) = 324

PV = PMT*(1 - (1+r)^-n)/r = 8,993.26*(1 - (1+0.5%)^-324)/0.5%

**PV = 1,441,261.05**

**Cost of refinancing =** 2%*remaining balance + 1,000 = (2%*1,441,261.05) + 1,000

Cost of refinancing = 29,825.22

**Monthly payment (if refinancing is done): **

PV = 1,441,261.05; r = 5%/12 = 0.4167%; n = 27*12 = 324

PMT = (1,441,261.05*0.4167%)/(1 -(1+0.4167%)^-324)

**PMT = 8,114.86**

**Balance remaining after 5 years (after refinancing):**

PMT = 8,114.86; r = 0.4167%; n = 22*12 = 264

PV = 8,114.86*(1-(1+0.4167%)^-264)/0.4167%

**PV = 1,297,794.91**

**Note: Cash flow table is attached below. **

**Using financial calculator:**

CF0 = -29,825.22;

CF1 = 878.40; N0 = 59 (5 years less one month);

CF2 = 19,668.80; N2 = 1, solve for IRR.

**IRR = 2.69%**

Hence,

**Annual IRR = 2.69%*12 = 32.29%**