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The basic computation here is incremental savings with compounded interest: take an initial amount, and at the end of each period add interest and an incremental payment. This continues for a number of periods, resulting in a final amount.

Debt repayment (for example, paying off a mortgage) is the identical calculation, but using a negative payment. Annuities are the same as debt repayment.

The computation involves 5 variables. You provide 4 of them, and the calculator computes the other one. The result is copied into “Scratchpad”.

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Initial (PV)	Interest %	Payment	Periods (N)	Final (FV)

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The basic formula for final value of incremental savings (for non-zero interest rate) is:

FV = PV * R^N + Y * (R^N - 1) / I, where
PV = initial value,
I  = periodic interest (as a fraction: 10% is 0.1),
Y  = periodic payment,
N  = number of periods,
FV = final value,
R  = 1 + I

This is easy to prove by induction, or by summing a geometric series. Solving for the other variables, except “I”, is trivial algebra. The calculator uses an iterative algorithm when it needs to compute “I”. Note that the displayed results have been rounded.

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