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Time to Exhaust PV

How long a fund lasts when making regular withdrawals.

When to use: Use to find how long retirement savings will last with annual withdrawals.

Calculator

Formula

n=ln(1PV×kPMT)ln(1+k)n = \frac{-\ln\left(1 - \frac{PV \times k}{PMT}\right)}{\ln(1 + k)}

Variables

SymbolNameDescriptionUnit
nNumber of YearsHow long the fund lastsyears
PVPresent ValueCurrent fund balance$
PMTPaymentAnnual withdrawal amount$
kInterest RateAnnual return%

Real-Life Examples

Example 1: Retirement Duration

You have $800,000 and withdraw $50,000/year at 5%. How long does it last?

Given

PV = 800,000PMT = 50,000k = 0.05

Step-by-Step

1.n = -ln(1 - 800000 × 0.05/50000) / ln(1.05)
2.n = -ln(1 - 0.8) / ln(1.05)
3.n = -ln(0.2) / 0.04879
4.n = 1.6094 / 0.04879
5.n = 32.99 years
Result:32.99

Your retirement fund will last about 33 years.

Example 2: Education Fund

$100,000 fund, withdraw $15,000/year at 4%. How long does it last?

Given

PV = 100,000PMT = 15,000k = 0.04

Step-by-Step

1.n = -ln(1 - 100000 × 0.04/15000) / ln(1.04)
2.n = -ln(0.7333) / 0.03922
3.n = 0.3101 / 0.03922
4.n = 7.91 years
Result:7.91

The education fund lasts about 7.91 years.

Frequently Asked Questions

Enter your current savings as PV, annual withdrawal as PMT, and expected return as k. The formula tells you how many years your money will last. Note: if PV × k ≥ PMT, the fund never runs out because interest covers the withdrawals.

The commonly cited 4% rule suggests withdrawing 4% of your initial balance annually (adjusted for inflation). At typical market returns, this has historically sustained a portfolio for 30+ years. However, individual circumstances and market conditions vary.

If withdrawals exceed interest, you are drawing down the principal. The balance decreases over time until it reaches zero. This formula calculates exactly when that happens.