Question

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 ​$4000 at the end of each year into a Roth IRA for the next 45 years. If you earn 7 percent compounded annually on your​ investment, how much will you have when you retire in 45 ​years? How much will you have if you wait 10 years before beginning to save and only make 35 payments into your retirement​ account? How much will you have when you retire in 45 ​years?

Answer 1

1)

Future value = Annuity * [(1 + r)ⁿ - 1] / r

Future value = 4,000 * [(1 + 0.07)⁴⁵ - 1] / 0.07

Future value = 4,000 * 285.749311

Future value = $1,142,997.24

You will have $1,142,997.24 in 45 years

2)

Future value = Annuity * [(1 + r)ⁿ - 1] / r

Future value = 4,000 * [(1 + 0.07)³⁵ - 1] / 0.07

Future value = 4,000 * 138.236878

Future value = $552,947.51

You will have $552,947.51 in 35 years