Step 1 :This question is equivalent to asking, 'What is the present value of $500,000 paid 10 years from now if the annually compounded interest rate is $5\%$?'
Step 2 :We can use the compound interest formula, $A(t)=p\left(1+\frac{r}{n}\right)^{n t}$, where $A(t)$ is the amount of money accumulated after n years, including interest, $p$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal), and $n$ is the number of times that interest is compounded per year.
Step 3 :In this case, we know that $A(t) = \$500,000$, $r = 0.05$, $n = 1$ (since the interest is compounded annually), and $t = 10$ years.
Step 4 :We can plug these values into the formula and solve for $p$.
Step 5 :So, $500,000 = p\left(1+\frac{0.05}{1}\right)^{1*10}$
Step 6 :Solving for $p$, we get $p = \frac{500,000}{(1+0.05)^{10}}$
Step 7 :Calculating the above expression, we get $p \approx \$306,956.63$
Step 8 :So, you should invest approximately \$306,956.63 to have \$500,000 in ten years at an annually compounded interest rate of $5\%$.
Step 9 :Expressing the answer as a dollar value rounded to the nearest cent, we get \(\boxed{\$306,956.63}\).