3 You are working for a finance firm and a client comes to you and wants to know how much money they should put in an annuity (which earns 4.56% interest compounded monthly) at the end of each month for the next 43 years. Their goal is that when they retire at the end of 43 years, they want the monthly withdrawals from the annuity to total $72,000 per year, and for the annuity is to last for the next 31 years. A. Determine the amount which your client needs to deposit into the annuity at the end of every month for the next 43 years so that they can meet their retirement goal. Show all your work that you used to answer this problem. Show your input variables when using the TVM solver and circle the variable you solved for. (10 points) B. Find the total amount of interest the client will earn (from the time they start contributing to the account to when they make the last withdrawal). Show how you arrived at the answer. (2 points) Extra Credit Problems EC1 When applying for a mortgage, find one that allows you to contribute more money than the required monthly payment. The following problems illustrate why: Let's say that you have a 30-year $418,250 fixed-rate mortgage at 5.11% interest compounded monthly. Instead of paying the regular monthly payment for the mortgage, you decide to add an additional $150 to each of your monthly payments. By paying the extra $150 a month, the extra amount in each payment is applied directly to reducing the principal. This means that (1) the length of the loan is reduced since the principal will be reduced faster (than if no extra amount was paid with your monthly payment) and (2) you eventually pay less in interest than if you were to pay only the regular monthly payment required. Answer the following: A. 8. Find out how many years it will take you to pay off the loan if you were to pay the additional $150 with each monthly payment? Use the TVM Solver. Show how you arrived at your answer. (1 point) How much money will you save in interest if you pay the additional $150 with each monthly payment than if you did not pay any additional amount each month? Show how you arrived at your answer and round it to the nearest dollar. (2 points) EC 2 If you roll a pair of dice and consider the sum of the two numbers, are the events "the sum is an odd number" and "the sum is 5, 6, or 7" independent? You must show your work to receive any credit on this question. (3 points)