Question $1$:

You have decided to begin planning for retirement in $35$ years. You opened a brokerage account for your IRA account and deposited $$25,000$ into your IRA account. At retirement you want to have $$1,500,000\mathrm{.}00$ accumulated in your IRA account and your IRA account is expected to earn $9\%$ per year. You are going to add the same amount at the end of every month to your IRA; what is the monthly payment to the nearest cent that you need to contribute to achieve your retirement goal of $$1,500,000?$ Do not enter $ or comma in the answer box. For example, if your answer is $$12,300\mathrm{.}456$ then enter as $12300\mathrm{.}46$ in the answer box.

$529\mathrm{.}22$

Question $2$:

Continue to use the data from problem $1,$ but now you altered your investment strategy to boost your expected earnings on your IRA account to $11\%$ per year and you plan to contribute the monthly amount at the beginning of each month rather than the end of each month. What is the new monthly payment to the nearest cent that you need to contribute to achieve your retirement goal of $$1,500,000?$ Do not enter $ or comma in the answer box. For example, if your answer is $$12,300\mathrm{.}456$ then enter as $12300\mathrm{.}46$ in the answer box.

Question $3$:

Continue to use the data from problem $1,$ but now you retired and have accumulated $$1,500,000\mathrm{.}00$ You altered your investment strategy to be more conservative in retirement and your expected earnings on your IRA account have been reduced to $8\%$ per year and you plan to live on the withdrawals from your IRA for the next $20$ years. You expect inflation to average $2\%$ per year and you want to withdraw a constant real amount of money annually at the beginning of each year starting today on the first day of your retirement. What amount can you withdraw today so that you can withdraw a constant real amount each year for the next $20$ years so that your IRA will be reduced to zero when you withdraw your $20$th withdrawal? Do not enter $ or comma in the answer box. For example, if your answer is $$12,300\mathrm{.}456$ then enter as $12300\mathrm{.}46$ in the answer box.