Compounding goes forward in time: FV = PV × (1+r)ⁿ. Discounting goes backward in time: PV = FV ÷ (1+r)ⁿ. Same r, same n, just inverted. If you can earn r on your money, then $1 today is identical to $1×(1+r)ⁿ in the future, and $1 in the future is identical to $1÷(1+r)ⁿ today. The two directions are not separate concepts — they are the same equation read left-to-right or right-to-left.
Present Value = Future Value ÷ (1 + r)ⁿ ← same arithmetic as compounding, run backward
The discount rate has two interchangeable framings — they always produce the same number. (1) Opportunity cost: "What is the return I am giving up by tying my money in this investment instead of the next-best alternative?" If your alternative is a Treasury bond paying 4%, your discount rate is 4%. (2) Risk-adjusted required return: "What return must this investment offer to compensate me for the risk and the wait?" If a startup is risky enough to demand 25% expected return, your discount rate is 25%. The CFA Institute uses framing (1); corporate finance textbooks usually start with (2). The math is identical.
Higher discount rate → lower present value of any future promise. This is the most consequential single fact in finance. When the Federal Reserve raises rates, the discount rate every investor uses creeps up. Future earnings of every company are discounted more harshly. Stock prices fall. Long-duration assets (growth tech, 30-year bonds, real estate with distant cash flows) fall harder than short-duration ones (banks, energy, dividend payers) because their cash flows are further out, so the higher discount applies more times. The 2022 selloff in long-duration tech stocks was textbook discount-rate mathematics, not a story about "AI" or "narrative."
| Future amount + horizon | PV at 3% | PV at 6% | PV at 10% | PV at 15% |
|---|---|---|---|---|
| $10,000 in 1 year | $9,709 | $9,434 | $9,091 | $8,696 |
| $10,000 in 5 years | $8,626 | $7,473 | $6,209 | $4,972 |
| $10,000 in 10 years | $7,441 | $5,584 | $3,855 | $2,472 |
| $10,000 in 20 years | $5,537 | $3,118 | $1,486 | $611 |
| $10,000 in 30 years | $4,120 | $1,741 | $573 | $151 |
Read the table by row OR by column to feel the two sensitivities. Read across a row: at any horizon, doubling the discount rate roughly halves the present value (compare 6% vs 12% — a 5x ratio shows up at 30 years because compounding the difference repeatedly matters). Read down a column: at any rate, doubling the horizon roughly squares the discount factor — a 30-year promise at 10% is worth ~6% of face. This is why "long-duration assets are interest-rate sensitive" — every additional year multiplies your exposure to discount-rate moves. A 1% rate move barely changes a 1-year PV. The same 1% move can swing a 30-year PV by 25%.
A practical implication: when you read "$1 trillion of student debt" or "$30 trillion national debt" or any other big future-dated number, ask quietly what discount rate the headline implies. A $1M payment due in 10 years has a present value of ~$386K at 10% and ~$744K at 3%. The same nominal liability can be a manageable burden or a crisis depending purely on prevailing rates. Politicians and the press routinely cite undiscounted nominal sums as if they are equivalent across decades — TVM literacy lets you reframe in your head.
Sit with the ideas.
Your opportunity cost falls from 8% to 4% (you can no longer earn 8% in safe alternatives). A relative still owes you $50,000 payable in 12 years. What happens to the present value of that promise?