Benjamin Franklin wrote of compounding: ". . . 'tis the stone that will turn all your lead into
gold. . . . Remember that money is of a prolific, generating nature. Money can beget money,
and its offspring can beget more."
n = number of compounding periods
i = periodic interest rate (decimal)
PV = present value
- FV = future value
PMT = periodic payment
1. This is the formula to calculate compound interest.
PV + PMT [ (1 - (1 + i)^ -n) / i] + FV (1 + i)^ -n = 0
2. This is the formula for finding n.
n = (ln (PMT - FV * i) - ln(PV * i - PMT)) / (ln (1+ i))
3. This is the formula for finding FV as a function of n.
FV = (-PV - PMT((1-(1+i)^(-n)) / i)) / ((1 + i) ^ (-n))
For the financial goal calculations, the rest of the variables have been replaced as follows.
FV with Financial Goal
PV with Initial Capital
PMT with Monthly Invested
i with ROI (annual rate of return on investment)
FV-(PV+nPMT) with Investment Gain