Ann would like to buy a house. It costs $800,000. Her down payment will be $40,0

Question

Ann would like to buy a house. It costs $800,000. Her down payment will be $40,000. She will take out a mortgage for $760,000. It will be a 30 year, fully amortizing, FRM, with constant monthly payments and monthly compounding. The annual interest rate is 4.00%. She must pay 2.5% in fees at the time of the loan.

1. Compute Ann’s annualized IRR for the mortgage in the spreadsheet. (Use the net cash flow.)

(1.a) What is the annualized IRR for the mortgage?

(1.b) Is it higher or lower than the mortgage contract rate?

(1.c) Why?

Explanation / Answer

Cost of house = 800,000

Down payment = 40,000

Loan required = 800,000 - 40,000 = 760,000

2.5% fee is required at the time of the loan

Actual amount of mortgage = 760,000/(1 - 0.025) = 779,487.18

PV = 779,487.18, N = 360, r = 0.04/12 = 0.01/3, FV = 0

PV = 779,487.18 = (PMT/(0.01/3)) * (1 - 1/(1 + 0.01/3)^360) + 0

PMT = 3,721.39

Ann has to pay $3,721.39 every month but she received loan $760,000 for her house

CF0 = -760,000

CF1-360 = 3,721.39

PV = 760,000, PMT = 3,721.39, N = 360, FV = 0;

Compute r = 0.003509 per month or 0.042110 per year

Annual effective rate = 4.21%

Annualized IRR = 4.21%

Mortgage rate is 4% but because of initial fee of 2.5% which puts additional cost on borrower, the effective rate rises to 4.21%

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