Johnny Dollar is trying to save for his retirement. He believes he can earn $7\%$ on average each year

on his retirement fund. Assume that at the beginning of each of the next $30$ years, Johnny will

allocate X dollars to his retirement fund. If at the beginning of a year Johnny has Y dollars in his

fund, by the end of the year, it will grow to $1\mathrm{.}07$ Y dollars.

a$)$ Develop a spreadsheet model to find out how much Johnny should allocate to his retirement fund

each year to ensure that he will have $$1$ million at the end of $30$ years. What is the total

contribution amount over $30$ years?

b$)$ Redo if the compound rate is $9\%$ per year. Compare total contribution amount to part $($a$).$

c$)$ Are there any key factors that are being ignored in our analysis of the amount saved for

retirement?