--%>
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 : Set of conflicts in reducing working

    Give an illustration of a set of conflicts encountered when attempting to reduce working capital?

    		•
  • Q : Explain market efficiency hypothesis

    According to what I read inside a book, market efficiency hypothesis means that the expected average value of variations is zero in the shares price. Thus, the best estimate of the future price of a share is its price now, as this incorporates all the available inform

    		•
  • Q : Could we explain that the shares’ value

    Could we explain that the shares’ value is intangible?

    		•
  • Q : Explain consensus among the chief

    Is there any consensus among the chief authors in finance concerning the market risk premium?

    		•
  • Q : Illustrates beta and capital structure

    We are valuing a company, many smaller than ours, so as to buy it. As that company is too smaller than ours this will have no influence on the capital structure and at the risk of the resulting company. It is the reason why I believe this the beta and the capital stru

    		•
  • Q : Which capital structure must consider

    Which capital structure must we consider when estimating the WACC for a subsidiary valuation: the one which is reasonable according to the risk of the subsidiary’s business that the average of the company or the one the subsidiary as “tolerates/per

    		•
  • Q : What is the Capital Cash Flow What is

    What is the Capital Cash Flow?

    		•
  • 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 : Affect the value of the stock Is the

     Is the value of this stock dependent on how long you plan to hold it? In other words, if your planned holding period were 2 years or 5 years rather than 3 years, would this affect the value of the stock today, P0? Explain your answer.<

    		•
  • Q : Calculated betas when they give

    Calculated betas give different information if they are acquired by using weekly, monthly or daily data.

    		•