Skip to content
SnapFi

Solve for Time

3 formulas

Solve-for-time formulas determine how many periods are needed to reach a financial target. Whether you want to know how long it takes for an investment to double, when you'll pay off a loan, or how many years of saving are required to hit a retirement goal, these formulas provide the answer.

Time from Lump Sum

Find how many years it takes for a present value to grow to a future value.

n=ln⁡(FV/PV)ln⁡(1+k)n = \frac{\ln(FV/PV)}{\ln(1 + k)}

Showing annual compounding

3 compounding options

Time to Reach FV Goal

How long to accumulate a target amount through regular annual payments.

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

Showing annual compounding

2 compounding options

Time to Exhaust PV

How long a fund lasts when making regular withdrawals.

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

Showing annual compounding

2 compounding options