EXAMPLE 1.4 Rate of Return and Rate of Return
Stereophonics, Inc., plans to borrow $20,000 from a bank for 1 year at 9% interest for new recording equipment. ( a ) Compute the interest and the total amount due after 1 year. ( b ) 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.
Solution
(a) Compute the total interest accrued by solving Equation [1.2] for interest accrued.
Interest = $20,000(0.09) = $1800
The total amount due is the sum of principal and interest.
Total due = $20,000 + 1800 = $21,800
(b) Figure 1–3 shows the values used in Equation [1.2]: $1800 interest, $20,000 original loan principal, 1-year interest period.
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| Figure 1–3 Values used to compute an interest rate of 9% per year. Example 1.4. |
Comment
Note that in part ( a ), the total amount due may also be computed as
Total due = principal(1 + interest rate) = $20,000(1.09) = $21,800
Later we will use this method to determine future amounts for times longer than one interest period.
From the perspective of a saver, a lender, or an investor, interest earned ( Figure 1–2 b ) is the fi nal amount minus the initial amount, or principal.
Interest earned total = amount now - principal
Interest earned over a specifi c 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.
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THE FUNDAMENTALS
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