--%>
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 : Types of Corporate Bonds What are the

    What are the various types of Corporate Bonds?

    		•
  • 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 : Define Working capital requirement

    Working capital requirement: Is a financial term known as WCR, which is used to judge the operational liquidity of the business and it is a part of operational capital. A firm in spite of having a good profitability and assets may not have a good liqu

    		•
  • Q : Financing EBIT problem Rusk Inc needs

    Rusk Inc needs $50 million in new capital that it might obtain by selling bonds at par with coupon of 12% or by selling stock at $40 (net) per share. The current capital structure of Rusk consists of $300 million (face value) of 10% coupon bonds selling at 90 and 10 m

    		•
  • 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 : Why classical option pricing required

    Why classical option pricing with constant volatility required?

    		•
  • Q : Calculate valuation realized by

    Is a valuation realized through a prestigious investment bank a scientifically approved result that any investor could utilize as a reference?

    		•
  • Q : Define capital goods Capital goods :

    Capital goods: Goods employed in producing other goods are termed as capital goods.

    		•
  • Q : Weighted return and simple return to

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

    		•
  • Q : APR of Loan When you take out an $8,000

    When you take out an $8,000 car loan that calls for 48 monthly payments of $225 each, then what is the APR of loan?

    		•