Emma will retire $3$ years from now. Her financial advisor advises her to take advantage of tax$-$free catch$-$up contributions to her individual retirement account $($IRA$).$ She can make a maximum catch$-$up contribution of $$6,000$ this year. Assume that this maximum contribution will remain at $$6,000$ for the next two years. Emma decides to make three contributions starting today $($i$.$e$.,$ she will make her first catch$-$up contribution of $$6,000$ today, a second contribution of $$6,000$ one year from today, and a third contribution two years from today$).$ Today is the day you are completing this assignment. How much will these three catch$-$up contributions accumulate to when she retires?

Explain your solution strategy by answering the following questions:

i$.$ Does this problem involve a lump sum, an annuity, or an uneven stream of cash flows?

ii$.$ Does it involve present value$($s$)$ or future value$($s$)?$

iii. Draw a timeline of the cash flows mentioned in the problem statement. Review the timelines in your textbook chapter if required.

iv$.$ What additional information would you need to provide a numerical answer for the question asked?

v$.$ Assuming you had that additional piece of information, how would you answer the question, How much will these three catch$-$up contributions accumulate to when she retires? Indicate the location of this value on your time line.