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In the s heyday of multi-leve l marketing schemes, one such. A participant had me rely. Those sub-agents would then recruit 6 sub-agents of their own. This would continue to an ever increasing number of levels. The expected profit base d on 9 levels of sub-agents was of the. There was n o in- dication in the brochure that to reach this level would require over 10,, 6 sub-agents. Reaching that level would definitely re- quire some compounding magic. When considering the equation.

If the unknown variable. If the unknown variable is the interest rate i , then solving for i. Financial calculators have functions that allow. When calculating interest accumulation over a fraction of a yea r or when executing short term financial transactions, a variation on com pound in- terest commonly known as simple interest is often used.

If t represents a fraction of a year, then under the application of simple interest, the accumulated value at ti me t of the initial invested amount of 1 is as follows. The accumulation function from time 0 to time t at annual simple in- terest rate i , where t is measured in years is. The following example refers to a promissory note , which is a short-term contract generally less than one year requiring the issuer of the note the borrower to pay the holder of the note the lender a principal amount plus interest on that principal at a specified annual interest rate for a specified length of time.

At the end of the time period the pay- ment principal and interest is due. Promissory note interest is calculated on the basis of simple interest. The interest rate earned by the lender is sometimes referred to as the yield rate earned on the investment.

In each case it will be important to relate the meaning of the yield rate to the context in which it is being used. Promissory note and simple interest. On January 31, Smith borrows from Brown and gives Brown a prom- issory note. On March 1, Brown sells the promissory note to Jones, who pays Brown a sum of money in return for the right to collect the payment from Smith on April Determine the amount Smith w as to have paid Brown on April Determine the amount that Jones paid to Brown and the yield rate interest rate Brown earned, quoted on an annual basis.

Assume all calculations are based on simple interest and a day year. Determine the amount that Jones paid. The payment required on the maturity date April 30 is. April 30 in a non-leap year; financial calculators often have a function that calculates the number of days between two dates. Let X denote the amount Jones pays Brown on March 1. We will de-. The following time-line diagram indicates the sequence of events.

January March 1. April Smith borrows from Brown. Brown receives X from Jones. Jones receives We are given. This inverse relationship between yield and price is typical of a fixed-income investment. A fixed-income investment is one for which the future payments are predetermined unlike an investment in, say, a stock, which involves some risk, and for which the return cannot be predetermined. Jones is in- vesting in a loan which will pay him If the desired interest rate for an investment with fixed future payments increases, the price that Jones is willing to pay for the investment decreases the less paid, the better the return on the investment.

An alternative way of describ- ing the inverse relationship between yield and price on fixed-income in- vestments is to say that the holder of a fixed income investment Brown will see the market value of the investment decrease if the yield rate to ma- turity demanded by a buyer Jones increases.

This can be explained by not- ing that a higher yield rate earned by Jones requires a smaller investment amount made by Jones to Brown to achieve the same dollar level of inter- est payments. This will be seen again when the notion of present value is discussed later in this chapter. Note that most banks use a day count even in the case of a leap year. From Equations 1. This is illustrated in Figure 1. From Figure 1.

The relationship between simple and compound interest is verifi ed alge-. In practice, interest accumulation is often based on a combinat ion of simple and compound interest. Compound interest would be applie d over the completed integer number of interest compounding periods, and simple interest would be applied from then to the fractional po int in the current interest period. When analyzing the accumulation of a single invested amount, the value of the investment is generally regarded as a function of time.

For example,. A t is the value of the investment at time t , with t usually measured in years. The amount by which the investment grows from time. Also, with this notation,. Accumulation can have any sort of pattern, and, as illustrated in Figure 1. The Dow Jones Average in Example 1. The graph indicates the Dow Jones index value on December 31 of each year based on an inves tment into the index of amount 1 on December 31, For the one-year peri- od from December 31, to December 31, the annual effec tive rate of interest is.

The relationship for. In other words:. The accumulated amount function can be used to find an effectiv e inter- est rate for any time interval. For example, the three-month ef fective in-. From a practical point of view, the accumulated amount function A t would be a step function, changing by discrete increments at each interest credit time point, since interest is credited or investment va lue is updat- ed at discrete points of time.

If we let X be the amount that must be invested at the start of a year to accumulate to 1 at the end of the year at annual effective inte rest rate i,. The amount. If the rate of interest for a period is i , the present valu e of an amount of. The factor. When a situation involves more than one interest rate, the symb ol. The present value factor is particularly important in the conte xt of compound interest. Accumulation under compound interest has the form.

This expression can be rewritten as. Kv is the present value at time 0 of an amount K due at time t when. Accumulation and present value are inverse processes of one another. Present value of 1 due in one period as a function of i. Present Value of 1 due in t periods as a function of t. The right graph in Figure 1. The left graph of Figure 1. Present value calculation.

Ted wants to invest a sufficient amount in a fund in order that the accumulated value will be one m illion dollars on his retirement date in 25 years. Ted considers two options. He can invest in Equity Mu tual Fund, which invests in the stock market. Fund has averaged an an- nual compound rate of return of The E.

Fund provides no guarantees as to its future performan ce. What amount must Ted invest if he chooses E. Fund and assumes that the average annual growth rate will continue for another 25 years? What amount must he invest if he opts for the stripped bond investment? Note that no sub-. The solution for i is. Solving for t. It is important to note that implicit in this expression. The present value based on simple interest accumulation assumes that inter- est begins accruing at the time the present value is being found.

There is no standard symbol representing present value under simple interest that corre- sponds to v under compound interest. Canadian Treasury bills — present value based on simple interest The figure below is an excerpt from the website of the Bank of Canada describing a sale of Treasury Bills by the Canadian federal government on Thursday, March 10, www.

A T-Bill is a debt obli- gation that requires the issuer to pay the owner a specified sum the face amount or amount on a specified date the maturity date. The issuer of the T-Bill is the borrower, the Canadian government in this case. The pur- chaser of the T-Bill would be an investment company or an individual.

Ca- nadian T-Bills are issued to mature in a number of days that is a multiple of 7. Canadian T-Bills are generally issued on a Thursday, and mature on a Thursday, mostly for periods of approximately 3 months, 6 months or 1 year. Treasury Bills — Regular Auction Results.

On behalf of the Minister of Finance, it was announced today that tenders for Government of Canada treasury bills have been acc epted as follows:. Auction Date. Date d'adjudication Heure limite de soumission Montant total. Bidding Deadline. Ratio de. Two T-Bills are described in Figure 1. The first one is set to mature June 18, , which is 98 days 14 weeks after issue. The yield is quoted as. The price is the present value, on the iss ue date, of due on the maturity date, and present value is calculated o n the basis of simple interest and a day year.

The quoted price based o n the quoted average yield rate of. The price of the second T-Bill can be found in a similar way. It matures September 10, , which is days 26 weeks after the issue date. The quoted average yield is. The price is. Valuation of Canadian T-Bills is algebraically identical to val uation of. We can generalize the notion of present value based on any accumulation.

The investment grows from amount. Therefore an amount of. In other words,. When a financial transaction is represented algebraically it is usually formu- lated by means of one or more equations that represent the values of the vari- ous components of the transaction and their interrelationships. Along with the interest rate, the other components of the transaction are the amounts dis- bursed and the amounts received.

These amounts can be thought o f as dated cash flows, in that both the amount and time of occurrenc e of each cash flow must be taken into account in an algebraic formulatio n. A mathematical representation of the transaction will be an equat ion that balances the dated cash outflows and inflows, according to the particu- lars of the transaction.

Such a balancing equation is called an equation of value for the transac- tion, and its formulation is a central element in the process o f analyzing a financial transaction. In order to formulate an equation of value for a transaction, i t is first nec- essary to choose a reference time point or valuation date. At t he refer- ence time point the equation of value balances, or equates, the following. Choice of valuation point for an equation of value. Un- fortunately for Walt, he loses each bet and agrees to repay his debt to the bookmaking service in four installments, to be made on March 7, 14, 21, and How muc h must Walt pay on March 28 to completely repay his debt?

The payments in the transaction are represented in Figure 1. We must choose a reference time point at which to formulate the equatio n of val- ue. All other amount s received and paid are in th e future,. The value at time 0 of what Wa lt will. Equating the value at time 0 of what Walt will receive with the value of what he will pay results in the equation.

Solving for X results in. The value of what. Walt has received is. Note that most financial transactions will have interest rates quoted as. The equivalent an nual effec-. We see from Example 1. Notice that Equatio n C can be. In general, when a transaction involves only compound inter-. For most transactions there will often be one reference time point that allows. Learn more about Scribd Membership Home. Read free for days Sign In.

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Ships from and sold by Amazon. Sold by ayvax and ships from Amazon Fulfillment. Customers who viewed this item also viewed. Page 1 of 1 Start over Page 1 of 1. Mathematics of Investment and Credit, 7th Edition. Only 5 left in stock - order soon. Broverman Only 2 left in stock - order soon. Leslie Jane Federer. Mathematics of Investment and Credit: 3rd Third edition.

Only 1 left in stock - order soon. Register a free business account. Product details Item Weight : 1. Tell the Publisher! I'd like to read this book on Kindle Don't have a Kindle? Customer reviews. How are ratings calculated? Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon.

It also analyzes reviews to verify trustworthiness. Top reviews Most recent Top reviews. Top reviews from the United States. There was a problem filtering reviews right now. Please try again later. Do not use it to learn options, swaps and derivatives. Verified Purchase. I am a math instructor trying to change his career to become an actuary. I bought the book to prepare myself for exam fm.

The algebraic proofs and the use of familiar notations are clear and easy to understand, so I find this book very useful. This is an incredibly invaluable text for FM prep. I wasn't able to get through all of the questions, but I loved it so much that when I returned the rental, I went ahead and got the 6th Edition in e-text.

It doesn't give as many examples on how to use the BA II Plus calculators for the problems, which was my only qualm. Great book overall. Needed for college. This textbook will prepare you for the FM 2 exam. I say prepare because the exercises in this tb are not equivalent to the hardness of the actual questions on the exam. Cht 6, 7, and 8 has some wrong and incomplete solutions.

The newer edition 4th also has the same errors. A highly approachable first testbook for studying the FM actuarial exam. An outstanding seller, I'd recommend to anyone. The book is an excellent one if you ready have a good calculus base in order to be able to make the connection between calculus and the formulas you will be using in calculating the rate and growth of the compound interest.

Mathematics of Investment and Credit. Bean, Michael A. Determinants of Interest Rates. Society of Actuaries, Interest Rate Swaps. Simple, compound, nominal and effective interest rates. Equation of value, actuarial notation. Derivatives, dividend discount model, short sale of stock, equity investments, financial derivatives.

Skip to main content. Search form Search. Course Description Course Information: An introductory course on financial mathematics, Math lays the foundation and prepares students for the series of courses required for the Financial Actuarial Mathematics major. Textbook s Broverman, Samuel A. Lecture Section Topics 1. Effective and nominal discount rates, force of interest. Determinants of interest rates. Level payment annuities.

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