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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.

Result

1.7908
$8,954.24

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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