--%>
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 : Problem on implied exchange rate a) The

    a) The Australian firm sold a ship to a Swiss firm and gave the Swiss client an option of paying either AUS10,000 or SF15,000 in 9 months. (i) In above, the Australian firm efficiently gave the Swiss client a free option to buy up

    		•
  • Q : Which taxes do I have to use for

    Which taxes do I have to utilize when calculating Free Cash Flow (FCF) – is this the medium tax rate or the marginal tax rate of the leveraged company?

    		•
  • Q : Calculated betas when they give

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

    		•
  • Q : Long-Term Debt What are Long-Term Debt

    What are Long-Term Debt and what are their main parts.

    		•
  • Q : Which parameter good measures value

    Which parameter good measures value creation; the Economic Value Added (EVA), the CVA (Cash Value Added) or the economic profit?

    		•
  • Q : Financial statements The concept of

    The concept of conservatism has been influential in the development of accounting theory and practice.  A major effect of conservatism is that accountants tend to recognize losses but not gains.  For example, when the value of an asset is impaired, it is wri

    		•
  • Q : Explain deducing yield curve model

    Explain deducing yield curve model of HJM.

    		•
  • Q : What is Financial Analysis Financial

    Financial Analysis: It is the investigation and interpretation of financial statements and associated financial reports. Trained and certified accountants generally complete this kind of analysis. The role of a financial analyst is to

    		•
  • Q : Does it make sense to apply identical

    The National Company responsible for the company where he work has newly published a document stating as that the levered beta of the sector of energy transportation is as 0.471870073 (it is 9 decimals). They acquired this number by considering the betas into the sect

    		•
  • Q : Problem on annual obligation payment

    ABC Corp. has a challenge: The CEO wants to set aside annual, end of year payments into a sinking fund account earning 5% over the next 6 years in order to retire $25 million in bonds that will be outstanding at that time. Determine the annual payment required each ye

    		•