Step 3: Calculate the Necessary Return on Investment
William has $8,000 a year to invest over the course of 25 years until his retirement. What return on his investment must he receive to turn $8,000 a year into $300,000 in 25 years? The answer can be calculated using the Future Value of an Annuity formula. An annuity is an investment (or payout) that is regularly occurring over time. Lottery payments, insurance premiums, and even one’s paycheck can be considered an annuity. The Future Value of an Annuity formula is given as:
FVA = CF * [((1 + r)n) / r]
where FVA is the future value of the annuity, CF is the cash flow (yearly investment), r is the rate of return, and n is the number of periods (years until retirement). Since William needs $300,000 (FVA) in 25 years (n) with an investment of $8,000 per year (CF), we need to solve for r to find the rate of return that will turn his investment into the anount he needs at retirement. Plugging these numbers into the formula above, we have:
300,000 = 8000 * [((1 + r)25) / r]
Solving for r we get 3.2138 or about 3.21%. To turn $8,000 a year for 25 years into $300,000 William needs to realize a yearly return of 3.21%.