A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
A dollar today is worth more than a dollar in the future because money held now can earn returns over time. Future Value = PV × (1 + r)n, where r is the interest rate per period and n is the number of periods. Present value discounts future cash flows back to today: PV = FV / (1 + r)n. This framework underlies every financial decision from comparing loan offers to evaluating investment returns.
Work through concrete scenarios: 'Would you rather have $1,000 today or $1,200 in three years if the going rate is 5%?' Calculate both answers. Then extend to longer time horizons to develop intuition for the exponential gap that accumulates.
You already understand percentages and exponents — you know that 5% means 5 per 100, and that exponents describe repeated multiplication. The time value of money is what happens when those two ideas meet the dimension of time. The core claim is that a dollar in hand today is more valuable than a dollar promised in the future — not because the future dollar is somehow worth less, but because the dollar you have now can *do work* in the meantime. Invested at any positive rate of return, it grows.
The future value formula puts a number to this intuition. If you put $1,000 in an account earning 5% per year, after one year you have $1,050. After two years, you earn interest on $1,050 — not just the original $1,000 — giving you $1,102.50. This is compound interest, the exponent in action: Future Value = PV × (1 + r)n. The exponent *n* (number of periods) is why time matters so much. At 7%, money doubles roughly every 10 years. $10,000 invested at 25 becomes $80,000 at 55 and $160,000 at 65 — purely from compounding, with nothing added. Wait until 35 to invest that same $10,000 and it only reaches $76,000 at 65. The ten-year head start is worth more than doubling the final balance.
Present value runs the formula in reverse: given a future amount, what is it worth in today's dollars? PV = FV / (1 + r)n. This is called discounting. If someone offers you $1,200 three years from now, and you could earn 5% elsewhere, what is that offer worth today? $1,200 / (1.05)3 ≈ $1,037. That's the present value — the amount you'd need to invest today at 5% to reach $1,200 in three years. If the price of getting that future $1,200 is more than $1,037, the deal isn't worth it at that discount rate. This comparison — present value versus cost — is the underlying logic of every financial decision involving future cash flows.
The practical power of this framework shows up everywhere. When a lottery jackpot advertises $10 million but the lump-sum option is $6 million, that's discounting — the $10 million paid out over 20 years has a present value of roughly $6 million at current interest rates. When you compare a 30-year mortgage to a 15-year mortgage, you're comparing different streams of cash flows discounted back to today. When a salesperson offers you "zero interest for 24 months," the time value of money is exactly what they're working around. Once you internalize that money has a time dimension, every offer involving future payments becomes a present-value comparison — and you have the tools to make that comparison.