Present Value
Present worth of a future sum.
Formula
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Example
To have $1000 in 5 years at 5%, invest 1000/1.05⁵ ≈ $783.53 today.
How it works
Present value tells you how much a future amount is worth in today’s money after accounting for growth over time. The idea is that money can earn interest, so a dollar received later is not equivalent to a dollar received now; dividing by (1 + r)^n reverses the effect of compounding. This formula is the backward-looking version of compound growth: if a sum becomes FV after n periods at rate r, then PV is the amount that would grow into that future sum.
When to use it
Use this formula when comparing money received at different times, such as valuing an investment, bond payment, or future savings goal. It is also useful in business decisions when you need to decide whether a future cash inflow is worth a certain amount today.
Worked example, step by step
Suppose you want to know the present value of $2,000 received in 3 years at an annual interest rate of 4%. PV = FV / (1 + r)^n PV = 2000 / (1 + 0.04)^3 PV = 2000 / 1.04^3 PV = 2000 / 1.124864 PV ≈ 1778.85 So, $2,000 received in 3 years is worth about $1,778.85 today.
Common mistakes to avoid
- Using r as a percent instead of converting it to a decimal
- Multiplying by (1 + r)^n instead of dividing by it
- Using the wrong number of periods, especially when the compounding period does not match the time unit
Did You Know?
Present value discounts future cash back to today — the foundation of valuing any investment.
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