Question 4 a) Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery. After income taxes he took home $1,000,000. Victor put the entire amount into an account earning 5% per year, compounded annually. He wants to quit his job, maintain his current lifestyle and withdraw enough at the BEGINNING of each year to replace his salary. At this rate, how long will his winnings last? Round your answer to the nearest whole year. \begin{tabular}{|l|l|l|l|} \hline N= & & \multirow{2}{*}{ How many years? } \\ \hline i/y= & & \\ \hline PV= & & \\ \hline PMT= & & \begin{tabular}{l} Remember to enter payment \\ as a negative amount! \end{tabular} \\ \hline FV= & & \end{tabular} b) Victoria Vogel (Victor's twin) also won the Wisconsin lottery but she did even better. The game she played paid $2,000,000 after taxes. Like Victor, she too put the entire amount in an account earning 5% per year, compounded annually. She will also withdraw $65,000 at the BEGINNING of each year. At this rate, how long will Victoria's winnings last? Round the answer to the nearest whole year. \begin{tabular}{|l|l|} \hline N= & \\ \hline i/y= & \\ \hline PV= & \\ \hline PMT= & \\ \hline FV= & \\ \hline \end{tabular} 1) What was your calculator's answer? Let's explore why we have this result: 2) How much does Victoria start the year with? 3) When does Victoria take her first payment, at the beginning or end of the year? 4) What is the amount of her withdrawal? 5) What is her new balance after the first withdrawal? Problem continues on next page 6) How much interest does Victoria earn at the end of year? Show work: Remember to enter payment as a negative amount Try three times; ask for help if needed. Question 5 8) Compare your results from 2 and 7 above. What may be the explanation for the Error? Explain