Discounting shrinks a future amount back to today
Money later is worth less than money now, because money now can earn a return. Present value reverses compounding: divide the future amount by the growth factor to find what it is worth today.
FV is the future amount, r the rate per period, and n the number of periods. At a positive rate, PV is always below FV, and the gap widens the further out the payment sits.
What $10,000 in 5 years is worth today
| Discount rate | Present value |
|---|---|
| 2% | $9,057 |
| 5% | $7,835 |
| 8% | $6,806 |
| 10% | $6,209 |
| 15% | $4,972 |
| 20% | $4,019 |
Same $10,000, same 5 years. A higher required return means you would pay less today to receive it, which is why the present value falls as the rate rises.
A stream of payments, and the perpetual case
- Annuity. For equal payments PMT each period, PV = PMT × [1 − (1 + r)−n] ÷ r. Used for loans, leases and pensions.
- Perpetuity. For a payment that never ends, it collapses to PV = PMT ÷ r. A $50 forever payment at 5% is worth $1,000 today.
- NPV. Discount every cash flow to today and add them up. A positive net present value means the investment clears its required return.
The mistake that ruins the answer
Keep the rate and the period on the same clock. A 12% annual rate is 1% a month, not 12% a month. Discounting 24 monthly cash flows at 12% instead of 1% understates their value by a wide margin.
- Nominal vs real. If you want today's buying power, discount with the real rate (roughly nominal minus inflation), not the nominal one.
- Round late. Rounding intermediate steps before the final answer introduces error that compounds over many periods.
Common questions
How do you calculate present value?
Divide the future amount by one plus the rate, raised to the number of periods: PV = FV divided by (1 + r) to the power n. For $10,000 in 5 years at 5%, that is 10,000 / 1.05^5, which is about $7,835.
What is the discount rate?
It is the annual return you would otherwise earn on the money, used to shrink a future amount back to today. It usually reflects your cost of capital or required rate of return. A higher rate means future money is worth less now.
Can I use a monthly rate instead of an annual one?
Yes, as long as the periods match. If you use a monthly rate, count the periods in months. Mixing an annual rate with monthly periods is the most common error and throws the answer off badly.
