What is Present Value?

Present Value is what a future amount of money is worth TODAY. R$ 1,000 in 1 year is worth less than R$ 1,000 today — because today you could invest it and have more in the future.

Formula

PV = FV ÷ (1 + i)^n

Where:

  • PV = Present Value
  • FV = Future Value
  • i = interest rate
  • n = number of periods

Practical example

Someone offers you R$ 10,000 in 2 years. With the Selic rate at 13% per year, what is it worth today?

PV = 10,000 ÷ (1.13)² = 10,000 ÷ 1.2769 = R$ 7,831

In other words: receiving R$ 10,000 in 2 years is the same as receiving R$ 7,831 today.

What it’s used for

  1. Comparing investments with different terms
  2. Evaluating proposals (“pay R$ 50,000 upfront or R$ 60,000 in 12 installments?”)
  3. Pricing fixed-income securities
  4. Business decisions (is this project worth it?)

Application in everyday life

When a store offers “12 installments with no interest of R$ 100 or R$ 1,000 upfront”:

  • 12 installments = R$ 1,200 in total
  • But the present value of 12 installments of R$ 100 is less than R$ 1,200
  • If you can invest the money at 1%/month, paying in installments and investing the difference is better

Simple rule

Money today is worth more than money tomorrow. Always consider the “cost of time” when making financial decisions.