The time value of money
Present value and future value
4 min
The compound-interest formula connects two points in time. Reading it forward gives future value; reading it backward gives present value. Mastering both directions is the whole game.
Future value — pushing money forward
Future value (FV) answers: how much will an amount today be worth later?
FV = PV * (1 + i)^n
Invest R$ 5,000 at 0.8% per month for 24 months:
FV = 5000 * (1.008)^24 = 5000 * 1.21036 = 6,051.81
Present value — pulling money back
Present value (PV) answers the reverse: how much is a future amount worth today? Rearranging the formula:
PV = FV / (1 + i)^n
You are promised R$ 6,051.81 in 24 months and the relevant rate is 0.8% per month:
PV = 6051.81 / (1.008)^24 = 6051.81 / 1.21036 = 5,000
The two operations are mirror images: FV scales an amount up by a growth factor, PV scales an amount down by the same factor.
Why this matters for investing
Every asset — a stock, a bond, a rental property — is ultimately worth the present value of the cash it is expected to produce. When you compare an investment that pays 1,000 units next year against one that pays 1,050 units in two years, you cannot compare them directly. You must bring both to today's value at the same rate first. That single discipline underlies valuation, the topic of the next lesson.
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