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The future-value formula $FV = PV(1+r)^n$ is rearranged by dividing both sides by the growth factor $(1+r)^n$. This isolates PV on one side, resulting in the present-value formula $PV = \frac{FV}{(1+r)^n}$.

Conditions: The original formula $FV = PV(1+r)^n$ holds true.; $(1+r)^n$ is not zero (which is true for standard positive interest rates).

The future-value formula $FV = PV(1+r)^n$ is rearranged by dividing both sides by the growth factor $(1+r)^n$. This isolates PV on one side, resulting in the present-value formula $PV = \frac{FV}{(1+r)^n}$.

Conditions: The original formula $FV = PV(1+r)^n$ holds true.; $(1+r)^n$ is not zero (which is true for standard positive interest rates).

To calculate the future value (FV) of a lump sum, you use the compound interest formula $FV = PV(1+r)^n$. You substitute the present value (PV), the interest rate per period (r), and the number of periods (n) into the formula.

Conditions: The interest rate r is assumed to remain constant over the period.; The compounding frequency matches the time unit of n (e.g., annual rate with years).; The formula assumes a single lump-sum payment rather than an annuity.

To calculate the future value (FV) of a lump sum, you use the compound interest formula $FV = PV(1+r)^n$. You substitute the present value (PV), the interest rate per period (r), and the number of periods (n) into the formula.

Conditions: The interest rate r is assumed to remain constant over the period.; The compounding frequency matches the time unit of n (e.g., annual rate with years).; The formula assumes a single lump-sum payment rather than an annuity.