Future Value Calculations

When a bond is sold between coupon dates, the price actually paid by an investor is equal to the present value of all future cash flows to be received. This value is greater than the quoted price by the amount of accrued interest, where the accrued interest is equal to the portion of the next coupon to be received that is owed to the original owner of the bond. The actual calculation of accrued interest depends on whether the security is a corporate security or a government security. 

Example Assume that a 9 percent coupon bond with a face value of 1,000 has just been purchased. Interest on this bond is paid semiannually, and it has been 45 days since the last coupon payment. What is the accrued interest on this bond  

This amount is added to the bond s quoted price to determine the amount actually paid by the purchaser. 

Example A Treasury bond with a face value of 100,000 is issued with a coupon rate of 8.75 percent. Coupon payment dates for this bond are November 15 and May 15. If this bond is purchased on January 5, what is the value of accrued interest  

There are 181 days between November 15 and May 15, and 184 days between May 15 and November 15. If the date of sale is included, there are 51 days between November 15 and January 5. The amount of accrued interest may be calculated as follows  

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Investments, CFD (cash flow diagram) comparing investments annuities, 271-272 at different times, 270-271 discount factors, 272-276 future value calculation, 274 cumulative, 269-270 definition, 0 discrete, 266-269... 

Based on these values, predict the interval within which 90% of all such values calculated in the future must fall. 

Portfolio value is maximized by appropriately prioritizing the projects within the portfolio based on the future potential financial value of each project multiplied by its probability of success. The future value of each development project is based on a calculation of its net present value (NPV). In this calculation, the anticipated financial return from the project is compared with that of an alternative investment of an equivalent amount of capital (8). The general equation for calculating NPV is... 

It should be noted here that the results of cluster calculations can at present only be qualitative in character. Energies and partial charges are not converged with respect to metal cluster size and level of approximation. The value of the calculations lies more in the opportunity to compare different ions with each other (in a given group) and the relative stability of different adsorption sites. The prediction of absolute adsorption energies is hardly possible. More promising for the future are calculations of adsorbates on periodic surfaces within the framework of the local density approximation of density functional theory (e.g.. Ref. 123). 

Solution. Firstly, let s see what a placement in a bank account can earn. Suppose that a placement at 10% for 5 years is found. The future value of the sum can be calculated with the Eq. 15.5 as F=1.0E6x(l+0.iy= 1.464E6E. 

If the order of the numerator M is greater than the order of the denominator N in Eq. (15.48), the calculation of requires future values of error. For example, if M N = 1, Eq. (15.49) tells us that we need to know or to calculate lUn or Since we do not know at time t what the error 6(/+7p will be one sampling period in the future, this calculation is physically impossible. 

Second, we calculate the posterior distribution, Pr( X). This distribution reflects what we learn about the unknown parameters once we have seen the data. Additionally, it will be used to predict the future unobserved outcome yo based on the corresponding measured features zq. A substantial advantage to using the posterior distribution to predict future values as opposed to using the maximum-likelihood values is that the former accounts for uncertainty in estimating the unknown parameters. In the third step, we evaluate how well the model fits the data, how the assumptions affect the results, and how reasonable the conclusions are. 

A key element of the description of a stochastic process is a specification of the level of informatimi oti the behaviour of prices that is available to an observer at each point in time. As with the martingale property, a calculation of the expected future values of a price process requires information on current prices. Generally, fmancial valuation models require data on both the current and the historical security prices, but investors are only able to deal on the basis of current known information and do not have access to future information. In a stochastic model, this concept is captured via the process known as filtration. 

The total interest earned during the eight-year life of this account is determined by calculating the dififtrence between the future value and the present deposit value. 

The discussion thus far has involved calculating future value given a known present value and rate of interest. For example, 100 invested today for one year at a simple interest rate of 6 percent will generate 100 X (1 + 0.06) = 106 at the end of the year. The future value of 100 in this case is 106. Conversely, 100 is the present value of 106, given the same term and interest rate. This relationship can be stated formally by rearranging equation (1.3) as shown in (1.7). 

Just as future and present value can be derived from one another, given an investment period and interest rate, so can the interest rate for a period be calculated given a present and a future value. The basic equation is merely rearranged again to solve for r. This, as will be discussed below, is known as the investment s yield. 

Discount factors can also be used to calculate the future value of a present investment by inverting the formula. In the example above, the six-month discount factor of 0.98756 signifies that 1 receivable in six months has a present value of 0.98756. By the same reasoning, 1 today would in six months be worth... 

Because the future values for the reference index are not known, it is not possible to calculate the redemption yield of an FRN. On the coupon-reset dates, the note will be priced precisely at par. Between these dates, it will trade very close to par, because of the way the coupon resets. If market rates rise between reset dates, the note will trade slightly below par if rates fall, it will trade slightly above par. This makes FRNs behavior very similar to that of money market instruments traded on a yield basis, although, of course, the notes have much longer maturities. FRNs can thus be viewed either as money market instruments or as alternatives to conventional bonds. Similarly, they can be analyzed using two approaches. 

The difficulty in calculating a bond s return is that its future value is not known with certainty, because it depends on the rates at which the interim cash flows can be reinvested, and these rates cannot be predicted. A number of approaches have been proposed that get around this. These are described in the following paragraphs, assuming simple interest rate environments. 

The result of Equation (22.30) is, under this assumption, the constant value of average solids velocity in the preloading regime. Comparison of the values calculated using a very simple Equation (22.30) and the values obtained by Roes and van Swaaij [4] for their experimental systems yields excellent agreement. Detailed discussion of this issue will be the subject of a future publication. 

It is necessary to distinguish between simple and compound interest. Simple interest is paid only on the deposit (L), whereas compound interest is where the bank pays interest on the principal deposit and the accumulated interest on the principal. Equation (12.3) is the future value of L calculated with compound interest. 

Two types of interest are used when calculating the future value of an investment. They are referred to as simple and compound interest. Sinple interest calculations are rarely used today. Unless specifically noted, all interest calculations will be carried out using conpound interest methods. 

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