Question

You just graduated and landed your first job in your new career. You remember that your favorite finance professor told you to begin the painless job of saving for retirement as soon as possible, so you decided to put away $2,000 at the end of each year in a Roth IRA. Your expected annual rate of return on the IRA is 7.5%. How much will you accumulate at retirement after 40 years of investing (note: this may assume that you are even retiring early)?

I am not using a financial calculator. Please show me the simplest solution.

Answer 1

Future Value of an Ordinary Annuity

The amount accumulated at retirement after 40 years is calculated using the Future Value of an Ordinary Annuity formula

Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r]

Annual Payment (P) = $2,000 per year

Interest rate (r) = 7.50% per year

Number of years (n) = 40 Years

Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r]

= $2,000 x [{(1 + 0.075)⁴⁰ – 1} / 0.075]

= $2,000 x [(18.04423 – 1) / 0.075]

= $2,000 x [17.04423 / 0.075]

= $2,000 x 227.25652

= $454,513

“Therefore, the total amount accumulated at retirement after 40 years would be $454,513”