Question

(Related to The Business of Life: Saving for Retirement) (Future value of an ordinary annuity) You are graduating from college at the end of this semester and after reading the The Business of Life box in this chapter, you have decided to invest $4,900 at the end of each year into a Roth IRA for the next 46 years. If you earn 10 percent compounded annually on your investment, how much will you have when you retire in 46 years? How much will you have if you wait 10 years before beginning to save and only make 36 payments into your retirement account? How much will you have when you retire in 46 years? $ (Round to the nearest cent.)

Answer 1

Future value of annuity = Annity amount * [((1+r)ⁿ – 1)/r]

Value of the investment after 46 years = $4900 * [((1+0.10)⁴⁶ – 1) / 0.10]

                                                                       = ;l.k/ $4900 * [(1.10⁴⁶-1)/0.10]

                                                                       = $4900 * [(80.1795-1)/0.10]

                                                                       = $4900*(79.1795/0.10)

                                                                       = $4900*791.795

                                                                      = $3,879,795.5

In case the investor waits for 10 years to start investment, ie., makes only 36 contributions

Value of investment after 36 years = $4900 * [((1+0.10)³⁶ – 1) / 0.10]

                                                               = $4900 * [(30.9126805 – 1)/0.10]

                                                               = $ 4900 * (29.9126805/0.10)

                                                               = $4900 * 299.126805

                                                               = $1,465,721.3