Is it possible to have one compound interest rate that would allow an investor to save $500 per month for 35 years and that same interest rate would allow him to withdraw, at retirement, $7,500 per month for 25 years? If so, what is such interest rate? Any help would be appreciated.
Yes! There can be such unique interest rate. However, it is relatively difficult to calculate such rate directly. Modern computers and calculators can find such rate if they are programmed correctly. In this case, for instance, you have to equate two different formulas. Namely, the first is to find the FV of $1 per period and the second is to find the PV of $1 per period as follows:
FV =500*(((1+R)^420 -1) / R) ....................................... (1)
PV =7500*(((1+R)^300-1) / (1+R)^300) / R)................(2)
Then, you would equate the above 2 formulas as follows:
500*(((1+R)^420 -1) / R) =7500*(((1+R)^300-1) / (1+R)^300) / R, solve for R
Through the process of iteration, the computer finds the interest rate, R, which comes to 0.00625 per month. Or, 0.00625 x 1200 =~7.50% compounded monthly.