Part $1$: Your Kindergartener comes to you with concerns about her retirement. She has learned of the concept of compounding by reading your textbook during her down time. Demonstrate compounding to your young finance student by calculating $($with Excel functions of course$)$ what the value of $$1,000$ at $3\%$ would be in $40$ years with annual, semi$-$annual, quarterly and monthly compounding. $($round to two decimal places$)$

Part $2$: After reviewing the compounding model, your Kindergartener has a follow up question about effective annual rates. She figures with more frequent compounding, the effective annual rate cannot be $3\%$ for all the compounding options. Calculate the effective annual rate for each of the compounding options in Question $8,$ using a function. $($round to three decimal places$)$