Nominal interest

A comparison of Eqs. (9-32) and (9-39) shows that the nominal interest rate i on a continuous basis is related to the effective interest rate i on an annual basis by... 

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 ... 

There is often some confusion in the use of the term interest rate. For instance, some banks advertise a given interest rate compounded daily. What this means is that the actual interest rate is the rate given divided by 365 and the period is one day. This is called the nominal interest rate, the amount that would be earned per year if the interest were not compounded ... 

The federal government requires that the nominal interest rate be stated by each lender. Example 10-8 shows how to determine an equivalent yearly interest rate when the period of compounding is less than a year. 

Both methods assume that the money earned can be reinvested at the nominal interest rate. Suppose the rates of return calculated are after tax returns and the company is generally earning a 5% or 6% return on investment. Is it reasonable to expect that all profits can be reinvested at 23% or even 20% No, it isn t Yet this is what is assumed in the Rate of Return method. Sometimes the rate of return may be as high as 50%, while a reasonable interest rate is less than 15%. Therefore if a reasonable value for the interest rate has been chosen (this is discussed later in this chapter) and the two methods differ, the results indicated by the Net Present Value method should be accepted. 

You wish to borrow 20,000 to build a home. The bank offers you a 20-year mortgage at 8% compounded monthly. What is your monthly payment What is the total interest that will be paid over 20 years Repeat the calculation for a IO-year and 30 year mortgage (note that the above is standard wording for the nominal interest). 

A finance company gives the following figures For a loan of 1,000 a person must make 36 monthly payments of 38.62 per month. What is the rate of return What is the nominal interest rate ... 

An interest rate quoted on an annual basis is called nominal interest. However, interest may be payable on a semiannual, quarterly monthly, or daily basis. To determine the amount compounded, the following equation applies ... 

Effective Interest Rates When an interest rate is quoted, it is nominal interest that is stated. These quotes are on an annual basis, however, when compounding occurs that is not the actual or effective interest. According to government regulations, an effec-... 

Example 6 Effective Interest Rate A person is quoted an 8.33 percent nominal interest rate on a 4-year loan compounded monthly Determine the effective interest rate. 

Nominal interest The number applied loosely to describe the annual interest rate. 

These capital cost factors were based on an assumption that each technology faces an 11 percent nominal interest rate, with 2 percent inflation in the economy, a marginal tax rate of 33 percent, a 10-year tax life, and a 20-year project life. 

Comparison among total amounts accumulated with simple interest, discrete compound interest, and continuous compound nominal interest. 

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. 

Nominal interest rates should always include a qualifying statement indicating the compounding period. For example, using the common annual basis, 100 invested at a nominal interest rate of 20 percent compounded annually would amount to 120.00 after 1 year if compounded semiannually, the amount would be 121.00 and, if compounded continuously, the amount would be 122.14. The corresponding effective interest rates are 20.00 percent, 21.00 percent, and 22.14 percent, respectively. 

If nominal interest rates are quoted, it is possible to determine the effective interest rate by proceeding from Eq. (5). 

In this equation, S represents the total amount of principal plus interest due after n periods at the periodic interest rate i. Let r be the nominal interest rate under conditions where there are m conversions or interest periods per year. 

By equating Eqs. (6) and (7), the following equation can be obtained for the effective interest rate in terms of the nominal interest rate and the number of periods per year ... 

Equations (6), (7), and (8) represent the basic expressions from which continuous-interest relationships can be developed. The symbol r represents the nominal interest rate with m interest periods per year. If the interest is compounded continuously, m approaches infinity, and Eq. (6) can be written as... 

Similarly, from Eq. (8), the effective annual interest rate which is the conventional interest rate that most executives comprehend, is expressed in terms of the nominal interest rate r compounded continuously as... 

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... 

Effective annual interest rates compared to equivalent nominal interest rates with continuous interest... 

As before, let r represent the nominal interest rate with m conversions or interest periods per year so that i = r/m and the total number of interest... 

Nominal interest rate with continuous compounding = r = 0.06 From Eq. (23),... 

In the tabulation of factors for continuous interest compounding and continuous cash flow, the nominal interest rate r is used for calculating the... 

What will be the total amount available 10 years from now if 2000 is deposited at the present time with nominal interest at the rate of 6 percent compounded semiannually ... 

By use of a digital computer, develop and present a printout of the data of effective interest versus nominal interest compounded continuously as given in Table 2. 

A) The case where the company demands a 20 percent continuous nominal interest rate of return after taxes on any investment [i.e., profitability index (r) is 20 percent]. 

---