The present value of $1,000 to be received in 5 years is ________ if the discount rate is 12.78%. (2024)

Certainly! I've got a strong grasp of financial concepts, particularly in the realm of present value calculations. This formula you've mentioned, PV = FV / (1 + r)^t, is fundamental in finance and accounting, particularly in evaluating the current worth of future cash flows. Let's break down the components:

1. Present Value (PV): This represents the current value of a sum of money that is to be received or paid in the future, adjusted for the time value of money.

2. Future Value (FV): This stands for the amount of money expected to be received or paid at a future date, assuming a certain interest rate or rate of return.

3. Rate (r): This is the interest rate or discount rate used to calculate the present value. It's crucial as it reflects the opportunity cost of receiving money in the future rather than today.

4. Time (t): This refers to the period over which the future value is calculated. It's usually in years but can be in any unit of time.

Now, using the formula you've provided: [PV = \frac{FV}{(1 + r)^t}]

Given:

• Future value (FV) = $1,000
• Rate (r) = 12.78% or 0.1278
• Time (t) = 5 years

Substituting these values into the formula gives us: [PV = \frac{1,000}{(1 + 0.1278)^5}]

Calculating further: [PV = \frac{1,000}{(1.1278)^5}] [PV ≈ \frac{1,000}{1.825}] [PV ≈ $548]

Thus, the present value, considering a discount rate of 12.78%, for $1,000 to be received in 5 years, is calculated to be $548.

This computation demonstrates the principle of discounting future cash flows to their present value, considering the time value of money, and how a higher discount rate reduces the present value of future cash flows.

If you need further clarification or have more finance-related questions, feel free to ask!