Financial Goal Calculations

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.

PV with Initial Capital
FV with Financial Goals
PMT with Monthly Invested
i with ROI (annual rate of return on investment)
FV-(PV+nPMT) with Investment Gain

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