Present Value Calculator Estimate the current worth of future cash — with 2025 discount rates, annuities, and perpetuitie...
Present Value Calculator
Estimate the current worth of future cash — with 2025 discount rates, annuities, and perpetuities.
Single Future Value**:
$$ PV = \frac{FV}{(1 + r)^n} $$
Ordinary Annuity**:
$$ PV = PMT \times \frac{1 - (1 + r)^{-n}}{r} $$
Growing Annuity (r ≠ g)**:
$$ PV = PMT \times \frac{1 - \left(\frac{1+g}{1+r}\right)^n}{r - g} $$
Perpetuity**:
$$ PV = \frac{PMT}{r} \quad \text{or} \quad PV = \frac{PMT}{r - g} \quad (r > g) $$
Example** ($1M in 30 yrs @ 7%): $$ PV = \frac{1{,}000{,}000}{(1.07)^{30}} = \mathbf{\$131{,}367} $$
✅ Pro Tip**: For inflation-adjusted cash flows, use *real rate* = (1 + nominal) / (1 + inflation) − 1.
⚠️ Avoid these common mistakes:
- Mixing nominal & real cash flows** — Use real rate with real cash flows (inflation-adjusted)
- Using arithmetic instead of geometric discounting** — Time value ≠ linear decay
- Ignoring compounding frequency** — 7% monthly ≠ 7% annual (7.23% effective)
- g ≥ r in perpetuities** — Formula blows up → no finite PV (e.g., 3% growth @ 2.5% rate)
✅ When to Use Each Mode**:
- Single FV**: Inheritance, bond maturity, lump-sum lottery
- Annuity**: Pension, structured settlement, mortgage payoff
- Growing Annuity**: Social Security COLA, COLA-adjusted pensions
- Perpetuity**: Preferred stock, endowment funds, dividend aristocrats
| Cash Flow | Rate | Term | PV |
|---|---|---|---|
| $1M (lump) | 7.0% | 30 yr | $131,367 |
| $50K/yr | 6.0% | 20 yr | $573,496 |
| $10K/yr +3% | 8.0% | 25 yr | $152,210 |
| $10K/yr (forever) | 5.0% | ∞ | $200,000 |
📉 Real vs. Nominal**:
- Nominal rate: 8.0%, Inflation: 3.0% → Real rate = 4.85%
- $50K/yr *in today’s dollars* for 20 yrs @ 4.85% = **$642,108 PV** (vs. $573,496 nominal)
➡️ Single Future Value
“$1M in 30 years @ 7% — what’s it worth today?” → **$131,367**
➡️ Annuity
“$50K/yr for 20 yrs @ 6% — PV?” → **$573,496** (ordinary), **$607,906** (due)
➡️ Growing Annuity
“$10K/yr growing 3% for 25 yrs @ 8% — PV?” → **$152,210**
➡️ Perpetuity
“$10K/yr forever @ 5% — PV?” → **$200,000**
Note: Uses exact financial formulas. Continuous compounding: $PV = FV \cdot e^{-rt}$. All rates assumed effective annual unless specified.