Retirement: If you assume a $3\%$ inflation rate over the next $45$ years and wanted to retire at such time with $$1$ million in today's dollars, you need to have saved approximately $$3,781,596.$ This is the future value of $$1$ million invested today at $3\%$ for $45$ years. It is unlikely that any of you have $$1$ million $($or much of anything$)$ to invest currently, so you will need to fund your retirement savings over the next $45$ years.

Please determine the following, assuming a $5\%$ return on investment and retirement in $45$ years.

$1.$ The equal annual contribution to your retirement fund over the next $45$ years to have accumulated $$3,781,596.($Use the Excel $"$PMT$"$ function.$)$

$2.$ You will find the answer from $1.$ to be far greater than any amount you will be able to fund, at least early in your career. Thus, compute the accumulated balance you would have in your retirement fund if you did the following.

a$.$ Contributed $$5,000$ annually for the first $10$ years of your career. $($Use the $"$FV$"$ function to determine the future value of this annuity in $10$ years. Then use the same $"$FV$"$ to determine future value of this amount in $35$ years.$)$

b$.$ Contributed $$10,000$ annually for the next $10$ years of your career. $($Use the $"$FV$"$ function to determine the future value of this annuity in $10$ years. Then use the same $"$FV$"$ to determine future value of this amount in $25$ years.$)$

c$.$ Contributed $$20,000$ annually for the next $10$ years of your career. $($Use the $"$FV$"$ function to determine the future value of this annuity in $10$ years. Then use the same $"$FV$"$ to determine future value of this amount in $15$ years.$)$

d$.$ Contributed $$40,000$ annually for the next $10$ years of your career. $($Use the $"$FV$"$ function to determine the future value of this annuity in $10$ years. Then use the same $"$FV$"$ to determine future value of this amount in $5$ years.$)$

Add up the amounts you determined in parts a$.$ thru d$.$ This should the balance in your retirement account at the end of $45$ years given the funding noted in a$.$ thru d$.$

$3.$ Based on the answers you determined in $1.$ and $2.,$ what conclusion can you make regarding your potential retirement?