Question

 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 ​$5,700 at the end of each year into a Roth IRA for the next 41 years. If you earn 9 percent compounded annually on your​ investment, how much will you have when you retire in 41 ​years? How much will you have if you wait 10 years before beginning to save and only make 31 payments into your retirement​ account?

How much will you have when you retire in 41 ​years?

Answer 1

Future Value of Annuity = Periodic Payment * {[(1+ r)^n - 1 ] / r }

where

rate of interest is 9% or 0.09

n is the number of years i.e 41

Periodic payment is 5700

Future Value of Annuity = 5700 * {[(1+ 0.09)^41 - 1 ] / 0.09 }

= 5700 * {33.23627 / 0.09}

= 5700 * 369.2919

= 2104963.63

Calculation of Future Value of Entity when saved and made 31 payments :

Future Value of Annuity = Periodic Payment * {[(1+ r)^n - 1 ] / r }

where

rate of interest is 9% or 0.09

n is the number of years i.e 31

Periodic payment is 5700

Future Value of Annuity = 5700 * {[(1+ 0.09)^31 - 1 ] / 0.09 }

= 5700 * {13.46177 / 0.09}

= 5700 * 149.5752

= 852578.74