--%>
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 : What are Stock exchanges Stock

    Stock exchanges: A stock exchange provides services useful for trading, issue and redemption of shares and other securities for traders and brokers. They will also provide facility for payment of income and dividends for listed securities. Securities

    		•
  • Q : Calculate their after tax cost of debt

    Your Corp, Inc. has a corporate tax rate of 35%. Please calculate their after tax cost of debt expressed as a percentage. Your Corp, Inc. has several outstanding bond issues all of whichrequire semiannual interest payments. Bond A has a coupon rate of 4.0%; a price qu

    		•
  • Q : Who published a book regarding

    Who published a book regarding option formula and risk neutrality?

    		•
  • Q : Is the given affirmation of an

    Is the given affirmation of an accountancy expert true? “There valuation criterion that reflects the value of the shares of a company in the most accurate way is based on the amount of the equity of shareholder of its balance sheet. Stating that the value of sha

    		•
  • Q : Earnings management What do you mean by

    What do you mean by Earnings management and what are their actions and activities?

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

    What is the Capital Cash Flow?

    		•
  • Q : Weighted return and simple return to

    What is the difference between weighted return and simple return to shareholders?

    		•
  • Q : Problem on financial manager

    Assume that you are a financial manager of Yuen Cheong Manufacturng Company. Due to the rising demand of product X, Yuen Cheong Manufacturng Company decides to open a new production plant in China, so it needs to take a loan of US$1 million. Bank A offers Yuen Cheong

    		•
  • Q : Regarding WACC Regarding the WACC which

    Regarding the WACC which has to be applied to a project, must it be an expected return, the average historical return or an opportunity cost on similar projects?

    		•
  • Q : Who were the creators of uncertain

    Who were the creators of uncertain volatility model?

    		•