--%>
Assignment Help - homework help

Problem on annual mortgage payment

You just took out a variable-rate mortgage on your new home. The mortgage value is $100,000, the term is 30 years, and initially the interest rate is 8%. The interest rate is fixed for 5 years, after which the time rate will be adjusted according to the prevailing rates. The latest rate can be exerted to your loan either by changing the amount payment or by changing the length of mortgage.

a) Supposing annual payments, what is the original annual mortgage payment?

b) Make an amortization schedule for the first 5 years. Then What is the mortgage balance after 5 years?

c) When the interest rate on mortgage changes to 9% after 5 years, then what will be the latest annual payment which keeps the similar termination time?

d) Under the interest change in part (c), what will be the new term if the payments remain the same?

E

Expert

Verified

a) The annual payment , M, can be computed using the following equation

1651_mp1.jpg

From the question, PV=$100,000 and r = 8% , substituting to the equation and we get
M = 100,000 / annuality factor (30,8%)
=> M = 100,000 / 11.26
=> M = $8,882.74

b)

1633_mp2.jpg

The balance after year 5 will be $96022.26-$1200.96 = $94,821.30

c) The PV of mortgage after year 5 is $94,821.30
Using the same formula as part a), let the new mortgage payment by M1

2430_mp3.jpg

From the question, PV= $94,821.30 and   = 9% , substituting to the equation and we get
 $94,821.30 / annulity factor (25,9%)
From Excel, we can compute the annuality factor, which is 9.823

M1 = $94,821.30/9.823 = $9,653.40

d) Using the same result in part (c ),

1636_mp4.jpg


From the question, PV= $94,821.30 and   = 9% , substituting to the equation and we get

1800_mp5.jpg

Solving the equation and we get T = 37.57
Therefore, it requires a total of 38 years to repay the mortgage if the payment remains the same.

   Related Questions in Corporate Finance

  • Q : Is the market risk premium a parameter

    Is the market risk premium a parameter, for the world economy or for the national economy?

    		•
  • Q : Zero coupon bonds problem Shana wants

    Shana wants to purchase 5-year zero coupon bonds with a face value of $1,000. Her opportunity cost is 8.5 %. Supposing annual compounding, what would be the present market price of such bonds? (Round to the closest dollar.) (a) $1,023  (b) $665  (c) $890&nbs

    		•
  • Q : Standard deviation of portfolios returns

    Assume that you have $50,000 which you want to invest in two companies, XYZ Books and ABC Audio. XYZ has a return of 10% and standard deviation 15%, while ABC has return of 15% with a standard deviation of 20%. The correlation coefficient between them is .5. Your port

    		•
  • Q : Vanilla Bonds-Corporate Bonds Define

    Define the term Vanilla Bonds regarding Corporate Bonds?

    		•
  • Q : Explain value of shares is Is this

    Is this correct that the value of the shares is, the “value of the results’ capitalization” that, as per to the Institute of Accounting and Auditing (ICAC) shows “the sum of the expected future results of the company throughout a certain period

    		•
  • Q : Working Capital - Current Assets and

    I do not know the meaning of Working Capital Requirements. I think this should be same to Working Capital (Current Assets – Current Liabilities). There am I right?

    		•
  • Q : Problem on exponential growth rate

    Atlanta Company stock is predicted to follow an exponential growth rate. The relationship among the current stock price P0, future price PT after time T, and continuously compounded rate of the return r, is: PT = P0eγT. The stock doesn’t pay any

    		•
  • Q : Is cash flow is a flow of cash to

    The often known as "cash flow" that is net income plus depreciation, is a flow of cash, but is this a flow to the company or to the shareholders?

    		•
  • Q : Market for Corporate Bonds Write some

    Write some point regarding Market for Corporate Bonds.

    		•
  • Q : Explain company creates value for its

    Is this true that a company creates value for its shareholders in a year when this distributes dividends or when the quotation of the shares increases?

    		•