Present Value Calculator
Present value answers one question: what is a future amount worth today? It is the foundation under every valuation, lease decision, settlement offer and capital budget.
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PV = FV ÷ (1 + r)^n
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Money Later Is Worth Less Than Money Now
Not because of inflation alone, but because money held now can be invested. At a 6% discount
rate:
| Amount received | In 5 years | In 10 years | In 20 years |
|---|---|---|---|
| $10,000 | $7,473 | $5,584 | $3,118 |
| $50,000 | $37,363 | $27,920 | $15,590 |
| $100,000 | $74,726 | $55,839 | $31,180 |
A promise of $100,000 in twenty years is worth about $31,000 today. That is why structured
settlements and lottery annuities pay so much less as a lump sum than their headline total.The Discount Rate Is the Whole Argument
Present value is arithmetic; the discount rate is a judgement, and it dominates the answer.
$100,000 in 20 years is worth $67,297 at 2%, $31,180 at 6%, and $14,864 at 10%.
Conventional choices: your cost of capital for a business decision, the risk-free rate plus a
risk premium for an investment, and your borrowing rate for a personal one. Anyone presenting
a present value without stating the rate has presented nothing.
Comparing Options Fairly
Present value is the only correct way to compare cash flows arriving at different times. A
$50,000 payout today, $60,000 in three years and $75,000 in seven are not comparable until
each is discounted to the same instant.
Where It Shows Up
Lease versus buy — discount the lease payments and compare with the purchase price.- Settlement offers — a lump sum against a payment stream.
- Pension elections — a lump sum against a lifetime annuity.
- Bond pricing — a bond's price *is* the present value of its coupons and principal.
- Capital projects — net present value, which is this calculation applied to every
inflow and outflow.The Limits
A present value assumes the future amount actually arrives. It says nothing about the credit
risk of whoever promised it, and a single discount rate cannot express "probably, unless the
counterparty fails."
The Projection Behind This Page
Starting from $10,000, adding $200 a month at 7%:
Year Deposited Balance Growth Growth on deposits 1 $12,400 $13,201 $801 6% 5 $22,000 $28,495 $6,495 30% 10 $34,000 $54,714 $20,714 61% 20 $58,000 $144,573 $86,573 149%
After 20 years, 60% of the balance is growth rather than money you
put in. That crossover — the point where returns exceed contributions — is the whole reason
compounding is worth waiting for, and it arrives later than most people expect.The Formula
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A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]
└── initial principal ──┘ └────── regular contributions ──────┘
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The second term usually dominates. On these numbers the $200 monthly contribution accounts for the larger share of the final balance, which is the practical lesson: how much you add matters more than the rate, right up until the balance gets large.