Equivalence A dollar has a date attached to it. Move that date and the number has to change. Draw the diagram, then read the answer off it.
CE 303 Engineering Economy
$
Direction
%
- Drawing
- Cash flow diagram
- Interest rate
- 5.00% per year
- Compounding
- Annual, discrete
- Span
- Year 0 to year 10
- Vertical scale
- Proportional to dollars
What it is worth in every year
| Year | Years moved | Factor | Equivalent worth |
|---|
Sensitivity to the interest rate
Reading the diagram
Two amounts on different dates are equivalent when, at the stated interest rate, you would just as soon have one as the other. Nothing is being earned or lost here — the same money is simply being quoted on a different date, the way a length can be quoted in feet or in metres.
Each year you move to the right, the amount is multiplied by one plus the interest rate. Each year you move to the left, it is divided by the same thing. That is the whole mechanism; the factor in parentheses is bookkeeping for how many times you did it.
The arrow you drew is the cash flow you know. The red arrow is the same money re-quoted on the year you asked about, and the red curve behind it is that quote taken at every year on the sheet. Arrows above the line are money coming in, arrows below it are money going out; a diagram is drawn from one party’s point of view, so pick a side and stay on it.
Click any year on the timeline to move the red arrow there.