Instructions: Complete the following sequence of problems. Introduction: This project explores the value of investing in a retirement plan such as a 401(k). A 401(k) functions (roughly) as an ordinary annuity, where the employee can contribute a portion of their salary to an account with annual compound interest, and the employer may match a portion of the employee contribution. Unlike most financial accounts, profits are not taxed, allowing the account to grow much more quickly. It should be noted that there are penalties for withdrawing before the age of 59 Question 1: Suppose a 65 year old wishes to invest in a payout annuity for their retirement. Their bank is offering an account with 7% interest compounded monthly. If they wish to receive $4000 each month for thirty years, how much should they invest? Question 2: Suppose a thirty-year old starts saving up for retirement; each year, they deposit $4000 in a bank account with 7% interest compounded annually; however, after accounting for taxes, the interest is effectively 6.5%. After 34 years, how much is in the account