Interest Rate and Rate of Return (ROR)
Interest is the manifestation of the time value of money. Computationally, interest is the difference between an ending amount of money and the beginning amount. If the difference is zero or negative, there is no interest. There are always two perspectives to an amount of interest—interest paid and interest earned. These are illustrated in Figure (1–2). Interest is paid when a person or organization borrowed money (obtained a loan) and repays a larger amount over time. Interest is earned when a person or organization saved, invested, or lent money and obtains a return of a larger amount over time. The numerical values and formulas used are the same for both perspectives, but the interpretations are different.
Interest paid on borrowed funds (a loan) is determined using the original amount, also called the principal,
When interest paid over a specific time unit is expressed as a percentage of the principal, the result is called the interest rate.
The time unit of the rate is called the interest period. By far the most common interest period used to state an interest rate is 1 year. Shorter time periods can be used, such as 1% per month. Thus, the interest period of the interest rate should always be included. If only the rate is stated, for example, 8.5%, a 1-year interest period is assumed.
Figure (1-2): (a) Interest paid over time to lender. (b) Interest earned over time by investor
An employee at LaserKinetics.com borrows $10,000 on May 1 and must repay a total of $10,700 exactly 1 year later. Determine the interest amount and the interest rate paid.
The perspective here is that of the borrower since $10,700 repays a loan. Apply Equation (1-1) to determine the interest paid.
Equation (1-2) determines the interest rate paid for 1 year.
Stereophonics, Inc., plans to borrow $20,000 from a bank for 1 year at 9% interest for new recording equipment.
1- Compute the interest and the total amount due after 1 year.
2- Construct a column graph that shows the original loan amount and total amount due after 1 year used to compute the loan interest rate of 9% per year.
1- Compute the total interest accrued by solving Equation (1-2) for interest accrued.
The total amount due is the sum of principal and interest.
2- Figure (1-3) shows the values used in Equation (1-2): $1800 interest, $20,000 original loan principal, 1-year interest period.
Figure (1-3): Values used to compute an interest rate of 9% per year.
From the perspective of a saver, a lender, or an investor, interest earned (Figure (1–2b)) is the final amount minus the initial amount, or principal.
Interest earned over a specific period of time is expressed as a percentage of the original amount and is called rate of return (ROR).
The time unit for rate of return is called the interest period, just as for the borrower’s perspective. Again, the most common period is 1 year. The term return on investment (ROI) is used equivalently with ROR in different industries and settings, especially where large capital funds are committed to engineering-oriented programs. The numerical values in Equations (1-2) and (1-4) are the same, but the term interest rate paid is more appropriate for the borrower’s perspective, while the rate of return earned is better for the investor’s perspective.
1- Calculate the amount deposited 1 year ago to have $1000 now at an interest rate of 5% per year.
2- Calculate the amount of interest earned during this time period.
1- The total amount accrued ($1000) is the sum of the original deposit and the earned interest. If X is the original deposit,
The original deposit is
2- Apply Equation (1-3) to determine the interest earned.
In Examples (1-2) to (1-4) the interest period was 1 year, and the interest amount was calculated at the end of one period. When more than one interest period is involved, e.g., the amount of interest after 3 years, it is necessary to state whether the interest is accrued on a simple or compound basis from one period to the next. This topic is covered later in this chapter.
Since inflation can significantly increase an interest rate, some comments about the fundamentals of inflation are warranted at this early stage. Inflation represents a decrease in the value of a given currency. That is, $10 now will not purchase the same amount of gasoline for your car (or most other things) as $10 did 10 years ago. The changing value of the currency affects market interest rates.