An athlete signs a contract that guarantees a \$12-million salary $7 \mathrm{yr}$ from now. Assuming that money can be invested at $5.3 \%$ with interest compounded continuously, what is the present value of that year's salary?

Step 1 ：Given that an athlete signs a contract that guarantees a $12-million salary 7 years from now. Assuming that money can be invested at 5.3% with interest compounded continuously, we are to find the present value of that year's salary.

Step 2 ：The present value of a future amount of money can be calculated using the formula for continuous compounding interest, which is: \(PV = FV * e^{-rt}\) where: \(PV\) is the present value, \(FV\) is the future value, \(r\) is the interest rate, \(t\) is the time in years, and \(e\) is the base of the natural logarithm, approximately equal to 2.71828.

Step 3 ：In this case, the future value (\(FV\)) is $12 million, the interest rate (\(r\)) is 5.3% or 0.053, and the time (\(t\)) is 7 years. We can substitute these values into the formula to find the present value.

Step 4 ：Substituting the given values into the formula, we get: \(PV = 12000000 * e^{-0.053*7}\)

Step 5 ：Solving the above expression, we get the present value (\(PV\)) as approximately \$8,280,527.30.

Step 6 ：This means that if this amount is invested today at a rate of 5.3% compounded continuously, it will grow to \$12 million in 7 years.

Step 7 ：Final Answer: The present value of the athlete's salary is approximately \(\boxed{8,280,527.30}\).