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Finance maths

Present value

What a future amount is worth today, by discounting it at an interest rate.

PV=FV(1+r)t
Future valueFV=PV(1+r)t

Calculator

The live calculator needs JavaScript. The worked example below shows the same steps it would.

What the symbols mean

PV
the present value: the amount today
FV
the future amount
r
the interest (discount) rate per period as a decimal
t
the number of periods

When to use it

Use it to compare money at different times: how much to invest today to have 10,000 in ten years, or whether a payment later is worth more than a smaller one now. It is compound interest run backwards.

Worked example

How much must be invested today at 5% a year to have 10,000 in 10 years?

  1. Start from the formula.

    PV=FV(1+r)t

  2. Substitute FV = 10,000.00, r = 0.05, t = 10 and work it out.

    PV=10,000.00(1+0.05)10
    =10,000.001.0510
    ≈6,139.13

Answer PV ≈ 6,139.13

Why it works

Investing PV at rate r for t periods gives PV(1+r)t. Setting that equal to FV and dividing gives the formula.

Common mistakes

  • Multiplying by (1+r)t instead of dividing; present value is smaller than future value (for r > 0).
  • Using a yearly rate with monthly periods; the rate and t must use the same period.
  • Adding up future payments without discounting each one.