To calculate the present worth (P) in engineering economic analysis, we utilize the formula that relates present value (P), annual cash flow (A), interest rate (i), and time period (n). The present worth is essentially the current value of a series of future cash flows, discounted back to the present using a specific interest rate.
In this scenario, we are given:
- P = 500
- A = 1.25
- i = 0.12 (or 12%)
- n = 25
The formula to find the present worth (P) can be defined as:
P = A × [(1 – (1 + i)^(-n)) / i]
Here’s how we plug in the values:
- Convert the interest rate to decimal: i = 12% = 0.12
- Substitute the values into the formula:
P = 1.25 × [(1 - (1 + 0.12)^(-25)) / 0.12]Now, calculate the expression within the brackets:
- (1 + 0.12) = 1.12
- 1.12^(-25) = 0.092593
- Now calculate: 1 – 0.092593 = 0.907407
- Divide this result by 0.12: 0.907407 / 0.12 = 7.562392
Finally, multiplying by A:
P = 1.25 × 7.562392 = 9.45299Thus, the present worth (P) at an interest rate of 12% over 25 years, with annual cash flow of 1.25 is approximately 9.45.