Final answer:
The present value of $40,000 to be received in eight years at an 8% interest rate is approximately $21,621.62 The calculation uses the present value formula that accounts for time value of money.
Step-by-step explanation:
The question asked by the student involves calculating the present value of $40,000 that the engineer is to receive in eight years, using an 8% interest rate. This is an application of the concept of the time value of money, which suggests that money available at the present time is worth more than the same amount in the future due to its potential earning capacity.
To calculate the present value, we use the formula:
PV = FV / (1 + r)^t
Where:
- PV is the present value
- FV is the future value ($40,000)
- r is the annual interest rate (8% or 0.08)
- t is the number of years (8 years)
Plugging in the values, we get:
PV = $40,000 / (1 + 0.08)^8
Calculating this we find that the present value the engineer should receive today is:
PV = $40,000 / (1.08)^8 ≈ $40,000 / 1.85093 ≈ $21,621.62
So, the engineer should receive approximately $21,621.62 today to have the equivalent amount of $40,000 in eight years at an 8% interest rate.