Question

Your goal is to become a millionaire by retirement. How much do you need to save each month to have $1,000,000 assuming you have 35 years to invest in an account that earns 7.5% real rate of return? If you earn $5,000/month, what percentage of your monthly income do you need to invest for retirement?

Answer 1

Desired Sum = $1,000,000
Time Period = 35 years or 420 months

Annual Interest Rate = 7.50%
Monthly Interest Rate = 7.50% / 12
Monthly Interest Rate = 0.625%

Let monthly saving be $x

$x*1.00625^419 + $x*1.00625^418 + …. + $x*1.00625 + $x = $1,000,000
$x * (1.00625^420 - 1) / 0.00625 = $1,000,000
$x * 2,030.762007 = $1,000,000
$x = $492.43

Monthly Saving = $492.43

Therefore, you need to save 9.85% ($492.43 / $5,000) of your salary each month in order to save $1,000,000 in 35 years.