Nominal interest rate

Short-Interval Compound Interest If interest payments become due m times per year at compound interest, mn payments are required in n years. The nominal annual interest rate Y is divided by m to give the effective interest rate per period. Hence,... 

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 ... 

Equation (9-113) shows that Eq. (9-114) is only approximately true and should be used, if at all, solely for low interest rates. Let us consider the case of a nominal (DCFRR) of 5 percent and an inflation rate of 3 percent. Equation (9-14) yields an approximate effective return rate of 2 percent, compared with the real effective rate of 1.94 percent given by Eq. (9-113) i.e., there is an error of 3.1 percent. Now let us consider the case of a nominal (DCFRR) of 2.5 percent and an inflation rate of 23 percent. Equation (9-114) yields an approximate effective return rate of 2 percent, compared with 1.63 percent from Eq. (9-113) in this case, the error that results is 22.7 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. 

Since the overdraft is payable daily at a nominal annual interest rate of 15 percent, it follows from Eq. (9-38) that the effective annual interest rate on overdraft = (1 -I- 0.15/365) — 1 = 16.18 percent. Similarly, the effective annual interest rate on deferred tax = (1 -I- 0.09/365) — 1 = 9.42 percent. 

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. 

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. 

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... 

Thus, with continuous interest compounding at a nominal annual interest rate of r, the amount S an intim principal P will compound to in n years isf ... 

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... 

Example 2 Calculations with continuous interest compounding. For the case of a nominal annual interest rate of20.00 percent, determine ... 

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),... 

For example, if the nominal continuous interest rate is 20 percent and the... 

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

---