Interest continuous compound

Continuous Compound Interest As m approaches infinity, the time interval between payments becomes infinitesimally small, and in the hmit Eq. (9-37) reduces to... 

Continuous Compound Interest In some companies, namely petroleum, petrochemical, and chemical companies, money transactions occur hourly or daily, or essentially continuously. The receipts from sales and services are invested immediately upon receipt. The interest on this cash flow is continuously compounded. To use continuous compounding when evaluating projects or investments, one assumes that cash flows continuously. 

The numerical difference between discrete compound interest and continuous compound interest is small, but when large sums of money are involved, the difference may be significant. Table 9-23 is an abbreviated continuous interest table, assuming that time zero is when start-up occurs. A summary of the equations for discrete compound and continuous compound interest is found in Table 9-24. 

Table 11 could be extended by the use of continuous compounding interest methods as outlined in Chaps. 7 and 10 to show the value of money to a company above which (or below which) material A would be selected over B, B... 

CONTINUOUS COMPOUNDING INTEREST FACTORS Interest Rate 9%... 

Continuous sensors, 1903-1904 Continuous-time dynamic-simulation, 128 Continuous timing, 1420 Continuous uniform cash flows compounded continuously (compound interest), 2345-2346... 

The Spot and Forward Rate Relationship In the discussion to date, we have assumed discrete time intervals and interest rates in discrete time. Here, we consider the relationship between spot and forward rates in continuous time. For this, we assume the mathematical convenience of a continuously compounded interest rate. 

We can then formulate a relationship between the continuously compounded interest rate and yield. It can be shown that... 

From elementary financial arithmetic, we know that an investment of 1 at a continuously compounded interest rate of r will have a value at time t given by so that the value of a coupon C at this time is given by... 

Effective continuous annual compovmd interest rate Amount of continuous compound interest... 

With continuous compound interest, the total amount of interest after Uy years is... 

In (1.6) e" is the exponentialfunction of rn. It represents the continuously compounded interest rate factor. To compute this factor for an interest rate of 6 percent over a term of one year, set r to 6 percent and to 1, giving... 

Expression (3.13) states that the bond price is a function of the continuously compounded interest rate. The r ht-hand side is the discount factor at time t. At t= T—that is, on the redemption date—the discount factor is 1, which is the redemption value of the bond and hence the price of the bond at that time. 

For the case of continuously compounded interest, we must look at what happens to Equation f9.9) as m... 

---