Question

Given an interest rate of 7% compounded annually, $4,000 to be received two years from today is equal to $ [blank]
today. (Round your answer to the nearest whole number.)

Answer 1

To calculate the present value of $4,000 to be received two years from today with an interest rate of 7% compounded annually, you can use the present value formula:

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

Where:
- \( PV \) = Present Value
- \( FV \) = Future Value ($4,000 in this case)
- \( r \) = interest rate (7% or 0.07)
- \( n \) = number of years (2 years)

Plugging in the values:

\[
PV = \frac{4000}{(1 + 0.07)^2}
\]

Calculating the denominator:

\[
(1 + 0.07)^2 = (1.07)^2 = 1.1449
\]

Now substitute this value back into the formula:

\[
PV = \frac{4000}{1.1449} \approx 3495.70
\]

Rounding to the nearest whole number, the present value is approximately:

\[
\boxed{3496}
\]

Thus, $4,000 to be received two years from today is equal to $3,496 today.