How is the future-value formula rearranged to solve for present value?

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).

Reasoning, step by step

1. Start with the future value equation: $FV = PV(1+r)^n$.
2. Identify the term multiplying PV, which is $(1+r)^n$.
3. Divide both sides of the equation by $(1+r)^n$.
4. Simplify the right side to isolate PV: $\frac{FV}{(1+r)^n} = PV$.
5. Rewrite as $PV = \frac{FV}{(1+r)^n}$.
6. Substitute the known values for FV, r, and n to compute PV.

Example

The video shows the board retaining $FV = PV(1+r)^n$ and then writing $PV = FV/(1+r)^n$. The speaker explains that to find the present value of $100,000 received in 10 years at 6%, you divide $100,000 by$(1.06)^{10}$.

Common misconceptions

• Subtracting $(1+r)^n$ instead of dividing.
• Forgetting that the exponent n applies to the entire term $(1+r)$.
• Assuming the rearrangement changes the underlying interest rate or time period.

Watch the explanation

Explore next

• What is the formula for present value used in this clip?
• What is the present value of $100,000 ten years from now at 6% annual interest?