Question

Katie and Ryan would both like to retire at age 60.

a) Katie turned 25 today. She would like to retire at age 60. If she starts investing $5,000 annually starting one year from now, with her last investment made on her 60th birthday, how much will she have at age 60 if she earns 5% compounded annually on her money? Show/explain your work.

b) Ryan turned 30 today. He would like to retire at age 60. If he starts investing $5,000 annually starting one year from now, with his last investment made on his 60th birthday, how much will he have at age 60 if he earns 5% compounded annually on his money? Show/explain your work.

c) In comparing the answers to a) and b), what conclusion do you draw?

Answer 1

This is the perfect example of Future Annuity. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate of return; it is the present value multiplied by the accumulation function.

1. Future Value of Annuity = P [ (1+r)^n – 1 / r]

                                                                = 5000 (1.05)^35-1/0.05

                                                                = 5000 * 90.32

                                                                = 451601

1. Future Value of Annuity = P [ (1+r)^n – 1 / r]

                                                                = 5000 (1.05)^30-1/0.05

                                                                = 5000 * 66.44

                                                                = 332194

1. A future annuity comes due on the annuity date. Katie has chosen to start investing at the age of 25 while Ryan has started investing at the age of 30.

Hence, there is a difference in the cash flow at retirement = 451601-332194 = 119407