(TIME VALUE OF MONEY)-PLEASE SOLVE ALL AND WITH ALL THE WORKINGS!

Question #1: You decide to invest $10,000 in a savings account, when the quoted interest rate is 3% effective and compounded annually. There is a so-called Rule of 72 which provides a guideline for determining how long it takes money to double, when it is being invested at a fixed rate. Namely, if you earn 3%, your money will double in 24 years (72 3 = 24), according to this widely used but inexact rule.

Part A: Please calculate the exact amount you will have in the savings account after 24 years? Is it more or less than $20,000? How inaccurate is the rule of 72? Use your calculations to verify and support your answers.

Part B: What if the 3% interest rate is an annual periodic rate (APR), and is compounded monthly (instead of annually)? How long will it take the $10,000 to double? Is the Rule of 72 relatively more or less accurate with more frequent compounding?