1. A forward thinking engineering junior who has studied economics decides that 2020 is the year to start saving for a future child to attend college. After running a few calculations, the engineer concludes that a spouse could be found, marriage proposed, and the children could be entering college in 2052. The plan is to collect $600 over the next year and invest it in July 2022 to be withdrawn in 30 years. Our forward thinking engineer is considering investing in a savings account at 0.5 % APR compounded yearly, a college savings account at 6% APR compounded monthly, or a mutual fund which matches the S&P 500's historical 10% annual return. For each investment option, a. Find the interest rate for a single compounding period, i b. Find the number of compounding periods, N c. Use Excel to calculate the future investment balance d. Show intermediate steps for part a, and b, and write the values used for the excel function in part c. e. Create a table of results for the three investment options