If you want to receive $1,000 in 3 years with an annual discount rate of 4%, what is the present value?

Understand the Problem

The question is asking to calculate the present value of an amount ($1,000) that is to be received in the future (3 years) given an annual discount rate (4%). This involves using the present value formula, which discounts the future amount back to the present value at the specified interest rate.

Answer

The present value is approximately $889.00.

Steps to Solve

Identify the Present Value Formula

The formula to calculate the present value (PV) is given by:

$$ PV = \frac{FV}{(1 + r)^n} $$

Where:

$FV$ = Future Value ($1,000 in this case)
$r$ = annual discount rate (4% or 0.04)
$n$ = number of years until the amount is received (3 years)

Substitute the Values into the Formula

Now, let's substitute the values into the present value formula:

$$ PV = \frac{1000}{(1 + 0.04)^3} $$

Calculate the Denominator

First, calculate the value of the denominator $(1 + 0.04)^3$:

$$ (1 + 0.04)^3 = 1.04^3 $$

Calculating this gives:

$$ 1.04^3 = 1.124864 $$

Compute the Present Value

Now, substitute this value back into the formula to find PV:

$$ PV = \frac{1000}{1.124864} $$

Calculating this gives:

$$ PV \approx 889.00 $$

The present value of $1,000 received in 3 years at an annual discount rate of 4% is approximately $889.00.

More Information

The present value tells us how much a future sum of money is worth today, considering the time value of money. This concept is widely used in finance to determine how much to invest today in order to reach a specific financial goal in the future.

Tips

Forgetting to convert the percentage rate into decimal form (4% should be 0.04).
Not raising the denominator to the power of the number of years ($n$).
Rounding errors when calculating powers or performing division.

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