Consider a cheque account. Initially, the amount of R 10 000 is deposited into the account....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider a cheque account. Initially, the amount of R 10 000 is deposited into the account. At the end of each month, interest is added at the rate of 2% per month to the amount of money that was in the account during the month. An additional deposit of N is added to the account at the end of each month, and the fixed amount R 500 is withdrawn from the account. Let An represent the amount of money in the account at the end of the month n, with Ao denoting the original amount. (6.1) Write down the difference equation for An (that is, an expression for An+1 in terms of An). Write down also, the initial value, A. (6.2) How should the value N be chosen such that there will always be money in the account? Justify your answer! Consider a house loan of R300 000, on which interest is charged at the rate of 1.5% per month at the end of the month; and a repayment of R3500 is made at the beginning of each month. Let An denote the amount of money still owing at the end of month n, with Ao denoting the original loan amount. (7.1) Write down the difference equation for An (that is, an expression for An+1 in terms of An). (7.2) Find the equilibrium point of the system. (7.3) Will the house loan eventually be paid off or not? Justify your answer! (7.4) Does the difference equation in (a) change (and if it does, how), if the following change is made to the situation: (a) Make the initial loan amount R500 000. (b) Change the repayment to R1600 per month. (c) Change the interest rate to 3% per month. Consider a cheque account. Initially, the amount of R 10 000 is deposited into the account. At the end of each month, interest is added at the rate of 2% per month to the amount of money that was in the account during the month. An additional deposit of N is added to the account at the end of each month, and the fixed amount R 500 is withdrawn from the account. Let An represent the amount of money in the account at the end of the month n, with Ao denoting the original amount. (6.1) Write down the difference equation for An (that is, an expression for An+1 in terms of An). Write down also, the initial value, A. (6.2) How should the value N be chosen such that there will always be money in the account? Justify your answer! Consider a house loan of R300 000, on which interest is charged at the rate of 1.5% per month at the end of the month; and a repayment of R3500 is made at the beginning of each month. Let An denote the amount of money still owing at the end of month n, with Ao denoting the original loan amount. (7.1) Write down the difference equation for An (that is, an expression for An+1 in terms of An). (7.2) Find the equilibrium point of the system. (7.3) Will the house loan eventually be paid off or not? Justify your answer! (7.4) Does the difference equation in (a) change (and if it does, how), if the following change is made to the situation: (a) Make the initial loan amount R500 000. (b) Change the repayment to R1600 per month. (c) Change the interest rate to 3% per month.
Expert Answer:
Related Book For
Financial Algebra advanced algebra with financial applications
ISBN: 978-0538449670
1st edition
Authors: Robert K. Gerver
Posted Date:
Students also viewed these accounting questions
-
The Crazy Eddie fraud may appear smaller and gentler than the massive billion-dollar frauds exposed in recent times, such as Bernie Madoffs Ponzi scheme, frauds in the subprime mortgage market, the...
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
8. Describe each of the following types of isomerism (i) geometrical isomerism (2 marks) (ii) solavate isomerism (2 marks) (iii) coordination isomerism (2 amrks)
-
Show that the sequence defined by an1 = 2, an+1 = 1/3 an satisfies 0 < an < 2and is decreasing. Deduce that the sequence is convergent and find its limit.
-
Were any problems unforeseeable?
-
Social networking has become a popular method of communication not only for individuals but for businesses as well. Visit the various social networking sites, such as Facebook and Twitter, and...
-
Identify each of the following accounts of Advanced Services Co. as asset, liability, owners equity, revenue, or expense, and state in each case whether the normal balance is a debit or a credit. a....
-
A man deposits $14,000 at the beginning of each year for 10 years in an account paying 5% compounded annually. He then puts the total amount on deposit in another account payin 6% compounded...
-
Compute P(E=Good) Compute P(S=Yes, H=Yes) Compute P(N=No, S=Yes, H=No, E=Good) (1) (2) (3) (4) (5) Compute P(E=Good|N=Yes) Compute P(E=Bad|S=No) P(N=Yes) P(N=No) 0.8 0.2 P(S=Yes) P(S=No) Party Last...
-
prove the following by "or conclusion" style (using the equivalence p -> (q or r) = (p && ~q) -> r) :let r be a real number, if r^2-9>0, then r > 0 or r < -3
-
What journal entry would be made to record the payment of \($1,500\) cash for factory utilities?
-
In what way do manufacturing firms and merchandising firms work together to provide end consumers with products?
-
Name the three types of business entities and briefly describe the nature of each.
-
Examine the sales and use tax statutes of your home state and determine the following: A. What is the type of sales tax imposed by the state? B. On whom is the legal imposition of the sales tax? C....
-
Which type of accounting would produce reports relevant to stockholders?
-
Please answer all parts with detailed explanation else downvote. . [The foiiowing information appiies to the questions dispiayed beiom] Farell is a member of Sierra Vista LLC. Although Sierra Vista...
-
In what ways does a well-designed enterprise search software vary from popular search engines (e.g., Bing, DuckDuckGo, and Google)?
-
Ralph earns $72,000 annually as an architect and is paid semimonthly. Alice also earns $72,000 but she is paid biweekly. a. How many more checks does Alice receive in a year when compared to Ralph?...
-
The Revreg Corporation pays an annual dividend of $1.60 per share. On Friday it closed at $44 per share with a net change of + 0.35. The dividend did not change. a. What was the yield on Friday? b....
-
On April 25, Berkshire Hathaway Inc closed at $126,875 per share. One year earlier, one share closed at $108,750. What was an approximate one-year percent change?
-
Financial planning models guide managers through the budget process so that managers do not need to really understand budgeting. Do you agree? Explain.
-
Identify the uses of a financial planning model.
-
Eckarts Runners Inc. has the following data: Accounts receivable, May 31: (0.3 x May sales of $400,000) = $120,000. Monthly forecasted sales: June, $400,000; July, $440,000; August, $500,000;...
Study smarter with the SolutionInn App