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Time to Exhaust PV

How long a fund lasts with periodic withdrawals.

When to use: Use for monthly withdrawal plans from retirement or investment accounts.

Calculator

Formula

n=−ln⁡(1−PV×(k/m)PMT)m×ln⁡(1+km)n = \frac{-\ln\left(1 - \frac{PV \times (k/m)}{PMT}\right)}{m \times \ln\left(1 + \frac{k}{m}\right)}

Variables

SymbolNameDescriptionUnit
nNumber of YearsHow long fund lastsyears
PVPresent ValueFund balance$
PMTPaymentMonthly withdrawal$
kInterest RateNominal annual rate%
mPeriods/YearWithdrawals per yearinteger

Real-Life Examples

Example 1: Monthly Retirement Withdrawals

$500,000 fund, withdraw $3,000/month at 5% monthly compounding.

Given

PV = 500,000PMT = 3,000k = 0.05m = 12

Step-by-Step

1.n = -ln(1 - 500000 × 0.004167/3000) / [12 × ln(1.004167)]
2.n = -ln(0.3056) / 0.04988
3.n = 1.1856 / 0.04988
4.n = 23.77 years
Result:23.76

Monthly withdrawals of $3,000 will last about 23.77 years.

Example 2: Emergency Fund Depletion

$50,000 fund, withdraw $2,000/month at 3% monthly compounding.

Given

PV = 50,000PMT = 2,000k = 0.03m = 12

Step-by-Step

1.n = -ln(1 - 50000 × 0.0025/2000) / [12 × ln(1.0025)]
2.n = -ln(0.9375) / 0.02996
3.n = 0.06454 / 0.02996
4.n = 2.15 years
Result:2.15

The emergency fund lasts about 2.15 years at $2,000/month.

Frequently Asked Questions

Enter your balance as PV, monthly withdrawal as PMT, annual rate as k, and 12 for m. The formula calculates how many years the fund sustains those monthly withdrawals before running out.

Monthly withdrawals deplete savings slightly faster than an equivalent annual withdrawal because money is removed earlier in the year, reducing the balance that earns interest. However, the difference is usually small.

If your monthly withdrawal is less than the monthly interest earned (PV × k/m), the fund will never run out — it actually grows over time. The formula only produces a finite result when withdrawals exceed interest income.

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