Putting It Together
Summary
Skeptics abound in this world, but even Einstein was “perplexed by the miracle of compound interest.” Your task is simply a future value problem.Examples
If you assume a continuous compounding interest (to simplify your calculations), your equation is:[latex]\displaystyle\int^{N}_{0}{Ke}^{r{(N-t)}}{dt}[/latex]
Where you invest K dollars per year for N years at interest rate r compounded continuously. You do not want to overplay your hand, so you use a modest rate of return of 8%.[latex]\displaystyle\int^{30}_{0}{10000e}^{0.08{(30-t)}}{dt}[/latex]
[latex]\displaystyle = \frac{{10000}}{{-0.08}}{e}^{0.08{(30-t)}}{\Biggr|}_{1}^{9}[/latex]
[latex]\displaystyle = \frac{{10000}}{{-0.08}}{(e}^{0.08{(30-30)}} - {e^{0.08{(30 - 0)}})}[/latex]
[latex] = \displaystyle\$1252897.05[/latex]
To strengthen your case for him to invest, you can redo these calculations for a 10% rate of return which would yield $1,908,553.69. Show him the math and let it speak for itself.