--%>
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 rules of the International

    RainFlower Trading Limited is a wholesaler of electronic calculators in Hong Kong. It has been importing goods from a Philippine manufacturer for eight years. The Philippine manufacturer had accepted payments in advance in the past. Recently, because of political turm

    		•
  • Q : What is the sales of the firm The

    The financial ratios of a firm are as follows. Current ratio = 1.33 Acid-test ratio = 0.80 Current liabilities = 40,000 Inventory turnover ratio = 6  What is the sales of the firm?

    		•
  • Q : Explain the definition of WACC An

    An investment bank computed my WACC. The report is as: “the definition of the WACC is defined as WACC = RF + βu (RM – RF); here RF being the risk-free rate and βu the unleveraged beta and RM the market risk rate.” It is differ from what we

    		•
  • Q : Define Credit and Collections Credit &

    Credit & Collections: Usually, credit is stated as the procedure of providing a loan, in which one party transfers wealth to the other with the expectation that it will be re-paid in full plus interest. The definition of collections is connected t

    		•
  • Q : What are Workpapers Workpapers : In

    Workpapers: In finance world, work papers are documents which are created during the procedure of computing the financial records of a business or individual. The accounting professional which is tasked with examining the book-keeping of a business mi

    		•
  • Q : Selling or purchasing problem Atlas

    Atlas Realty Company is interested in buying a house and renting it out for $12,000 a year, collecting the rent in advance each year. This will depreciate the house over 25 years; however sell it after 15 years at twice its purchase price. The maintenance expenditures

    		•
  • Q : Problem on sales collections The 2010

    The 2010 income statements of Leggett and Platt, inc. reports net sales of $4,076.1 million in 2010 and $4,250 million in 2009. The balance sheet reports accounts and other receivables, net of $550.5 million at December 31, 2010 and $640.2 million at December 31, 2009

    		•
  • Q : Marketing Decisions & Profitability

    Marketing Decisions Assignment:  Email the answers to the following questions in an attached word document using the proper file name format as follows:  1   

    		•
  • Q : How you can predict future evolution of

    Could we suppose that, as we cannot predict the future evolution of the value of shares, a good estimation would be to consider this constant during the next five years?

    		•
  • 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?

    		•