Question
At 1/1/2020, you take out a mortgage loan of $233,000. Your mortgage broker informs you that you can borrow the rest using a 20-year mortgage
At 1/1/2020, you take out a mortgage loan of $233,000. Your mortgage broker informs you that you can borrow the rest using a 20-year mortgage at an effective annual interest rate of 5%, with monthly compounding and constant monthly payments.
You may ignore all taxes and fees for the entirety of this problem. Note that today is t = 0 and after you buy the house you will make the first payment one month from now (t = 1).
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a) Calculate the monthly payment on your home.
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b) How much of your 1st payment goes toward paying down principal? How much goes toward
paying interest?
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c) How much of your 60th payment goes toward paying down principal? How much goes toward
paying interest?
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d) What is the present value of remaining principal balance after you make your 60th payment
(at t = 60)?
Now, suppose you just make your 60th payment. There are still 180 payments remaining. Now, the Federal Reserve announces that the market interest rate is reset to 0%. However, you are still facing the same payment schedule.
e) At the new discount rate of 0%, what is the present value of your remaining payments?
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