### Instruction: A man nearing retirement wants to invest some money in a fund that compounds annually at a rate of 6 percent, so that in five years, he will have at least $\$100,000$.  How much money must he invest now to make that happen?  (Give your answer to the nearest dollar.).### Response: I need to find the present value of $\$100,000$ in five years, using the formula $PV = FV/(1 + r)^n$, where $PV$ is the present value, $FV$ is the future value, $r$ is the annual interest rate, and $n$ is the number of years.
Plugging in the given values, I get $PV = 100000/(1 + 0.06)^5$.
To simplify the expression, I can use the exponent rules to rewrite $(1 + 0.06)^5$ as $1.06^5$.
Using a calculator, I find that $1.06^5 \approx 1.33823$, so $PV \approx 100000/1.33823$.
Dividing, I get $PV \approx 74720.80$.
Rounding to the nearest dollar, the answer is $\$74721$.