Calculate, to the nearest cent, the future value of an investment of $\$ 10,000$ at the stated interest rate after the stated amount of time. [HINT: See Quick Examples 1 and \(2 .\). \(11.2 \%\) per year, compounded monthly, after 12 years

Use a time value of money utility (a calculator, spreadsheet, or the Website). Such a utility can solve for any of the inputs, given values for the others. Alonzo plans to retire as soon as he has accumulated \(\$ 250,000\) through quarterly payments of \(\$ 2,500 .\) If Alonzo invests this money at \(5.4 \%\) interest, compounded quarterly, when (to the nearest year) can he retire?

Are based on the following chart, which shows monthly figures for Apple stock in \(2010:^{4}\) Marked are the following points on the chart: $$\begin{array}{|c|c|c|c|c|c|}\hline \text { Jan. 10 } & \text { Feb. 10 } & \text { Mar. 10 } & \text { Apr.10} & \text { May 10 } & \text { June 10 } \\\\\hline 211.98 & 195.46 & 218.95 & 235.97 & 235.86 &255.96 \\\\\hline \text { July 10 } & \text { Aug. 10 } & \text { Sep. 10 } & \text { Oct. 10 } & \text { Nov.10 } & \text { Dec. 10 } \\\\\hline 246.94 & 260.09 & 258.77 & 294.07 & 317.13 & 317.44 \\\\\hline\end{array}$$ Suppose you bought Apple stock in April. If you later sold at one of the marked dates on the chart, which of those dates would have given you the largest monthly return (on a simple interest basis), and what would that return have been?

Your other cousin Cecilia claims that you will earn more interest by depositing \(\$ 10,000\) through smaller, more frequent payments than through larger less frequent payments. Is she correct? Give a reason for your answer.

Retirement Plans and Trusts Exercises \(45-54\) are based on the following table, which shows the average returns for some of the largest mutual funds commonly found in retirement plans. \(^{20}\) (Assume end-of-month deposits and withdrawals and monthly compounding, and assume that the quoted rate of return continues indefinitely.) $$ \begin{array}{|r|c|c|c|c|} \hline \begin{array}{r} \text { Mutual } \\ \text { Fund } \end{array} & \begin{array}{c} \text { Fidelity } \\ \text { Growth } \\ \text { Company } \end{array} & \begin{array}{c} \text { Vanguard } \\ 500 \text { Index } \end{array} & \begin{array}{c} \text { PIMCO } \\ \text { Total Return } \end{array} & \begin{array}{c} \text { Vanguard } \\ \text { Total Bond } \\ \text { Market Index } \end{array} \\ \hline \begin{array}{r} \text { Rate of } \\ \text { Return } \end{array} & 14.83 \% & 13.25 \% & 2.77 \% & 2.67 \% \\ \hline \text { Type } & \text { Stock fund } & \text { Stock fund } & \text { Bond fund } & \text { Bond fund } \\ \hline \end{array} $$ How much would be accumulated after 25 years in a retirement account invested entirely in the Vanguard stock fund with payments of \(\$ 380\) per month? [HINT: See Quick Example \(1 .]\)

Are based on the following chart, which shows monthly figures for Apple stock in \(2010:^{4}\) Marked are the following points on the chart: $$\begin{array}{|c|c|c|c|c|c|}\hline \text { Jan. 10 } & \text { Feb. 10 } & \text { Mar. 10 } & \text { Apr.10} & \text { May 10 } & \text { June 10 } \\\\\hline 211.98 & 195.46 & 218.95 & 235.97 & 235.86 &255.96 \\\\\hline \text { July 10 } & \text { Aug. 10 } & \text { Sep. 10 } & \text { Oct. 10 } & \text { Nov.10 } & \text { Dec. 10 } \\\\\hline 246.94 & 260.09 & 258.77 & 294.07 & 317.13 & 317.44 \\\\\hline\end{array}$$ Calculate to the nearest \(0.01 \%\) your monthly percentage return (on a simple interest basis) if you had bought Apple stock in February and sold in June.