Compound elapsed years

Estimate elapsed years and compounding periods required to reach a target future value.

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Calculation specification

Reviewed on:

Formula basis

For periodic rate i, periods p=log(FV/PV)/log(1+i) and years=p/k. Nominal input uses i=r/k; effective input uses i=(1+R)^(1/k)−1.

Calculation method

Uses logarithms to derive the years and compounding periods required for principal to reach a target under the selected rate definition.

Exclusions and checks required

  • A valid logarithmic solution may not exist when the rate and target direction are inconsistent.
  • Rate changes, tax, fees, cash flows, and conversion of fractional periods to actual dates are excluded.

Example input:：Time for JPY 1 million to reach JPY 1.5 million with monthly compounding

annualRate
5
compoundRateType
nominal
principal
1000000
futureValue
1500000
periodsPerYear
12
digits
10

The continuous year display is not an actual transaction date.

FAQ

Who is this calculator for? Compound elapsed years

Estimate elapsed years and compounding periods required to reach a target future value.

What values should I enter?

Applies to: Compound interest / n = log(FV/PV) ÷ {k × log(1+r/k)}

How should I interpret this estimate?

Uses logarithms to derive the years and compounding periods required for principal to reach a target under the selected rate definition.

How to use

  1. Enter your input values and press Calculate.
  2. Review the result and compare it with expected context.
  3. For periodic rate i, periods p=log(FV/PV)/log(1+i) and years=p/k. Nominal input uses i=r/k; effective input uses i=(1+R)^(1/k)−1.