Time and Mary Essay Example for Free

Time and Mary Essay Mary has been working for a university for almost 25 years and is now approaching retirement. She wants to address several financial issues before her retirement and has asked you to help her resolve the situations below. Her assignment to you is to provide a 4-5 page report, addressing each of the following issues separately. You are to show all your calculations and provide a detailed explanation for each issue. Issue A: For the last 19 years, Mary has been depositing $500 in her savings account , which has earned 5% per year, compounded annually and is expected to continue paying that amount. Mary will make one more $500 deposit one year from today. If Mary closes the account right after she makes the last deposit, how much will this account be worth at that time? Future Value of Annuity = P (1+i)n – 1 i = $500 (1. 05)20 – 1 .05 = $500 (1. 653) (0. 5) =$500 x (33. 065) =$16,533 Issue B: Mary has been working at the university for 25 years, with an excellent record of service. As a result, the board wants to reward her with a bonus to her retirement package. They are offering her $75,000 a year for 20 years, starting one year from her retirement date and each year for 19 years after that date. Mary would prefer a one-time payment the day after she retires. What would this amount be if the appropriate interest rate is 7%? Present Value of Annuity = P 1 – (1+i)-n i = $75,000 1 – (1. 07)-20 .07 = $75,000 0. 741 .07 =$75,000 x (10. 594) =$794,550 If Mary was to receive a one-time payment the day after she retires, she would receive $794,550. But if she takes $75,000 a year for 20 years it would equal to $1,500,000 ($75,000x20yrs) Issue C: Mary’s replacement is unexpectedly hired away by another school, and Mary is asked to stay in her position for another three years. The board assumes the bonus should stay the same, but Mary knows the present value of her bonus will change. What would be the present value of her deferred annuity? Payment will be deferred for 3 years. Present Value = FV 1 (1+i)n= 794,550 1 (1. 07)3 = 794,550 x 0. 816 = $648,590 Issue D: Mary wants to help pay for her granddaughter Beth’s education. She has decided to pay for half of the tuition costs at State University, which are now $11,000 per year. Tuition is expected to increase at a rate of 7% per year into the foreseeable future. Beth just had her 12th birthday. Beth plans to 1 / 2 start college on her 18th birthday and finish in four years. Mary will make a deposit today and continue making deposits each year until Beth starts college. The account will earn 4% interest, compounded annually. How much must Mary’s deposits be each year in order to pay half of Beth’s tuition at the beginning of each school each year? Future Value = PV (1+i)n = 11,000 (1+. 07)10 = 11,000 x 1. 967 = $21,639 Present Value = FV 1 (1+i)n= 11,000 1 (1+. 04)10 = 11,000 x 0. 675 = $7,425 Mary must deposit $7,425 each year in order to pay half of $21,639; which will be Beth’s overall tuition for college. POWERED BY TCPDF (WWW. TCPDF. ORG).