Interest annual compound

In the above example, the discount rate used was the annual compound interest rate offered by the bank. In business investment opportunities the appropriate discount rate is the cost of capital to the company. This may be calculated in different ways, but should always reflect how much it costs the oil company to borrow the money which it uses to invest in its projects. This may be a weighted average of the cost of the share capital and loan capital of a company. 

Annual Compound Interest It is more common to use compound interest, in which F and P are related by... 

Numerically, the difference between continuous and annual compounding is small. In practice, it is probably far smaller than the errors in the estimated cash-flow data. Annual compound interest conforms more closely to current acceptable accounting practice. However, the small difference between continuous and annual compounding may be significant when apphed to very large sums of money. 

Let us suppose that 100 is invested at a nominal interest rate of 5 percent. We then compute the future worth of the investment after 2 years and also compute the effective annual interest rate for the following lands of interest (I) simple, (2) annual compound, (3) monthly compound, (4) daily compound, and (5) continuous compound. The following tabulation shows the results of the calculations, along with the appropriate equation to be used ... 

Example 1 Capitalized Cost of Equipment Apiece of equipment has been installed at a cost of 100,000 and is expected to have a working life of 10 years with a scrap value of 20,000. Let us calculate the capitalized cost of the equipment based on an annual compound-interest rate of 5 percent. 

Bills are due on monthly account with a 2 percent discount for cash. Overdraft and deferred-tax interest are compounded daily at nominal annual interest rates of 15 and 9 percent respectively. Corporation tax, capital gains tax, and personal income tax rates are 50, 40, and 30 percent respectively. The current rate of inflation is at 8 percent per year. The traditional return expected hy investors is 7 percent per year net of all taxes in real terms. 

A shortage of cash may prevent a company from taking advantage of large discounts available for bulk purchase of raw materials. The importance of the availability of adequate cash or near cash can be seen by considering an account payable within 28 days, with a 2 percent discount allowed if paid within 7 days. If cash is not available to pay the account within 7 days, this is then equivalent to paying 2 percent interest on the money for the remaining 21-day period, or an annual compound-interest rate of more than 41 percent. 

To provide for the college education of a child, what annual interest rate must you obtain to have a current investment of 5000 grow to become 10,000 in 8 years if the interest is compounded annually ... 

You open a savings account today (the middle of the month) with a 775 deposit. The account pays 6 % interest (annual value) compounded semimonthly. If you make semimonthly deposits of 50 beginning next month, how long will it take for your account to reach 4000 ... 

The problems in this section assume the use of the simple-interest formula, compounded annually. In actuality, financial institutions use compound interest and computer programs to figure out these problems. But you get a good idea of how it works — and a pretty good estimate of the actual answer using the less complex simple-interest formula. 

Suppose that you invested 6.02 x 1023 so that it earned 1% compound interest annually. How much money would you have at the end often years ... 

It is desirable to express the exact interest rate based on the original principal and the convenient time unit of 1 year. A rate of this type is known as the effective interest rate. In common engineering practice, it is usually preferable to deal with effective interest rates rather than with nominal interest rates. The only time that nominal and effective interest rates are equal is when the interest is compounded annually. 

As is illustrated in the following example, a conventional interest rate (i.e., effective annual interest rate) of 22.14 percent is equivalent to a 20.00 percent nominal interest rate compounded continuously. Note, also, that a nominal interest rate compounded daily gives results very close to those obtained with... 

An annuity due is being used to accumulate money. Interest is compounded at an effective annual rate of 8 percent, and 1000 is deposited at the beginning of each year. What will the total amount of the annuity due be after 5 years ... 

Note In this example, interest WQS compounded annually on Qfl end-of-year basis and continuous interest compounding was ignored. Also, construction period an( land value were not considered. The preceding effects could have been included in the analysis for a more sophisticated treatment using the methods presented in Examples 2 and 3 of this chapter. 

Simple interest forgoes the money earned by annual compounding and is rarely used in engineering... 

This factor is used to find the equivalent future worth, F, of a present value, P, when the interest is continuously compounded at the nominal annual rate of r%. For example, consider the problem of finding the future worth in six years of 5,000 invested now at 9% nominal interest rate compounded continuously. 

Effective discrete compound interest Effective discrete annual compound interest rate... 

If the interest rate is 3%/quarter, then with four quarters per year, the nominal interest rate, r, is 0.03(4) = 0.12 or 12%/yr. In the case of simple interest (no compounding), 1,000 at the beginning of a year would yield 1,000(1.12) = 1,200. But, more commonly, nominal interest rates are stated on an annual basis with a compounding period, for example, 12% compounded quarterly. 

If it is assumed that 200,000 will be needed for a 4-yr college education starting 10 yr from now, how much must be invested today at a 6% nominal annual interest rate compounded (a) continuously, and (b) twice annually ... 

Note that the minimum capital is obtained when the interest is compounded continuously, with a difference of 980, between it and the result for semi-annual compounding. ... 

The terminal value for quarterly compounding is thus about 13 cents more than that for annual compounded interest. 

The effective annual interest rate is greater than the nominal annual rate. This indicates that the effective interest rate will continue to increase as the number of conpounding periods per year increases. For the limiting case, interest is compounded continuously. 

Volume II of Organic Reac tions an annual series that reviews reactions of interest to organic chemists contains the statement Most organic compounds burn or explode when brought in contact with fluorine... 

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