If you win $20,000 annually for 15 years, what is the present value of that amount if your desired rate of return is 7%?

To determine the present value of winning $20,000 annually for 15 years at a rate of return of 7%, you need to apply the present value of an annuity formula, which helps calculate the value today of a series of future cash flows.

The formula for the present value of an annuity is:

[ PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) ]

Where:

• ( PV ) is the present value

• ( P ) is the annual payment ($20,000 in this case)

• ( r ) is the rate of return (0.07 for a 7% rate)

• ( n ) is the number of years (15)

Substituting the values into the formula gives:

[ PV = 20,000 \times \left( \frac{1 - (1 + 0.07)^{-15}}{0.07} \right) ]

Calculating the components:

1. Calculate ( (1 + 0.07)^{-15} )

2. Calculate the entire fraction ( \left( \frac{1 - (1 + 0.07)