--%>
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 price share and stock

    Brittney and Kim Wan Sun have successfully launched a successful talent agency, ABC. They expect the firm’s earnings and dividends to grow by 20% annually for the next 10 years and they establish a strong base and to grow at a constant 5% per year thereafter. AB

    		•
  • Q : Calculating Beta when market

    A company with a market capitalization of $100 million has no debt and a beta of 0.8. What will its beta be after it borrows $50 million (giving that there are no other changes and no taxes)?

    		•
  • Q : Explain Financial Management Financial

    Financial Management: It means organizing, planning, directing and controlling the financial activities like procurement and use of funds of enterprise. This means exerting general management principles to the financial resources of enterprise. <

    		•
  • Q : Explain Indenture Explain the term

    Explain the term Indenture and also describe their provisions?

    		•
  • Q : Variance of a portfolio The variance of

    The variance of a portfolio of 40 stocks will be the addition of _______ variance terms and _______ covariance terms. A) 40; 1560B) 40; 1600C) 80; 40D) 1600; 40

    		•
  • Q : Explain method to analyze and to value

    Are there any methods to analyze and to value seasonal businesses?

    		•
  • Q : Problem regarding purchasing machine

    Alger Corp needs to buy some construction equipment for $50,000 that has a helpful life of 4 years with no salvage value. The Alger utilizes straight-line depreciation. Alger contains a tax rate of 30%, and it employs a discount rate of 10%. The equipment will produce

    		•
  • Q : Is book value the excellent proxy to

    Is book value the excellent proxy to the value of the shares?

    		•
  • Q : Problem on required rate of return

    Tudor Online Publishing Corporation has tax rate of 35%, debt-to-equity ratio of 25%, and has (leveraged) beta 1.25. The riskless rate is 3% and the market return is 12%. Windsor Publishing Company is an all equity company and is in the same business. What is the requ

    		•
  • Q : Zero Coupon Bonds-Corporate Bonds

    Describe the term Zero Coupon Bonds in Corporate Bonds?

    		•