Final answer:
The present value is calculated using the formula PV = FV / (1+i)^n, which helps in determining the current worth of a future sum considering a specific interest rate and period. An example calculation for a future value of $3,000 with an 8% interest rate over 5 years would apply this formula to find the present value.
Step-by-step explanation:
The formula for present value (PV) is used to determine the current worth of a specific amount of money that will be received in the future, taking into account a specific interest rate over a certain period of time. The basic formula is derived by rearranging the compound interest formula:
PV(1+i)^n = FV
Where:
- PV is the present value.
- FV is the future value.
- i is the interest rate per period.
- n is the number of periods.
Therefore, to find the present value, the formula is simplified to:
PV = FV / (1+i)^n
For example, to calculate the present value of a future sum, such as $3,000, that is expected to be received in 5 years with an annual interest rate of 8%, the calculation would be:
PV = $3,000 / (1 + 0.08)^5
To calculate the present discounted value of future profits, you would apply this formula to each time period when a benefit is expected to be received and then add up all the present values for the different time periods for a final answer.