--%>
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 : 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 : Historical return on stock market and

    The market risk premium is difference among the historical return upon the stock market and the risk-free rate, for yearly. Why is this negative for some years?

    		•
  • Q : What is nonlinearity in option pricing

    What is nonlinearity in option pricing model?

    		•
  • Q : Which currency is utilized in an

    Which currency has to be utilized in an international acquisition in order to compute the flows?

    		•
  • Q : Problem on common stock The AB Corp

    The AB Corp stock has a β of 1.15 and it will pay a dividend of $2.50 next year. The expected rate of return of the market is 17% and the current riskless rate is 9%. The expected rate of progress of AB is 4%. Find the value of its common stock.

    		•
  • Q : Yield to maturity problem Jenny is

    Jenny is looking to invest in some 5-year bonds which pay annual coupons of 6.25 % and are presently selling at $912.34. What is the present market yield on these bonds? (Round to the closest Answer.) (1) 9.5%  (2) 8.5%  (3) 6.5%  (4) 7.5%

  • Q : Efficiency Ratios Efficiency Ratios :

    Efficiency Ratios: These ratios comprise Receivables Turnover, Inventory Turnover, Asset Turnover and Net Working Capital Turnover ratios. Efficiency ratios show the utilization of Assets of the company thus as to generate Revenue that is, the best ut

    		•
  • Q : Who explained the high-peak/fat-tails

    Who explained the high-peak/fat-tails?

    		•
  • Q : Explain consensus among the chief

    Is there any consensus among the chief authors in finance concerning the market risk premium?

    		•
  • Q : Explain the result of volatility

    Explain the result of volatility structure.

    		•