Time and Mary
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)
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)
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)
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