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Compound Amount Factor Calculator

Enter the interest rate per period, number of periods and an optional principal to get the compound amount factor and future value.

How it is calculated

The factor is F/P = (1 + i)n, where i is the interest rate per period entered as a percentage (6 means 6%, divided by 100 internally) and n is the number of compounding periods. Rate and periods must use the same time unit: a monthly rate needs months, an annual rate needs years. The factor is shown to 4 decimals. If you also enter a principal P greater than zero, the future value is FV = P × (1 + i)n, calculated from the unrounded factor and shown in dollars; with no principal the future value shows a dash. Periods cannot be negative and the rate must be above -100%, otherwise there is no result. Fractional periods are accepted.

Worked example

Take a 6% rate per year over 10 years with a principal of 5000. First divide the rate by 100 to get 0.06, then raise 1.06 to the 10th power. That gives a compound amount factor of 1.7908. Multiplying the principal by the unrounded factor, 5000 × 1.790848, gives a future value of $8,954.24. In other words every dollar invested today grows to about 1.79 dollars after ten years of annual compounding.

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Common mistakes

  • Typing the rate as a decimal (0.06) instead of a percentage (6). The tool divides by 100, so 0.06 means 0.06% and the factor will be almost 1.
  • Mixing units, for example entering an annual rate with a number of months. Convert so that both are per the same period (monthly rate with months, or annual rate with years).
  • Using the nominal annual rate with monthly periods. Divide the annual rate by 12 first, or the factor will be far too large.
  • Reading the factor as money. It is a pure multiplier; the dollar figure only appears when a principal is entered.
  • Expecting a result for a rate of -100% or lower, or for negative periods. These inputs return nothing.

Sources

About this calculator

This calculator computes the single-payment compound amount factor, written (F/P, i, n) in engineering economics notation, using the formula (1 + i)ⁿ. It's the multiplier that grows a present sum of money into its future value after n compounding periods at interest rate i per period — the mirror image of the present worth (P/F) factor.

Engineers, accountants and financial analysts use this factor as a building block in time-value-of-money calculations, capital budgeting and engineering economic comparisons, often pulling it straight from interest-factor tables.

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