Irish Calculators
Loans & mortgages

Annuity Present and Future Value Factor Calculator

Calculate the multiplier that converts equal payments into a present or future value. These are financial factors, not prices or guarantees for an insurer's lifetime annuity.

Runs privately in your browserMethod reviewed

Your numbers

Your figures stay on this device.

How the calculation works

Calculate present-value and future-value multipliers for equal periodic payments. Each factor values one currency unit paid per period, allowing you to scale a known payment without pricing an insurance product.

PV factor = [1 − (1+i)^−n]/i; FV factor = [(1+i)^n − 1]/i. Beginning payments multiply either factor by (1+i); zero-rate factors equal n.

  1. Define the payment timeline

    End payments form an ordinary annuity; beginning payments form an annuity due. Keep that timing consistent when relating a factor to a cash-flow series.

  2. Calculate present value

    The present-value factor sums the discounted value of one unit per payment. At zero rate, there is no discounting and the factor equals the payment count.

  3. Calculate future value

    The future-value factor accumulates unit payments to the term end. Beginning-payment factors multiply the equivalent end-payment factor by one plus the period rate.

Worked example: Zero-rate factor

Sample inputs demonstrate the method. They are not a forecast or product offer.

The first example contains ten payments with a zero period rate. Without discounting or growth, both factors equal ten. Ten unit payments have a total value of ten at either endpoint under that assumption.

Interest rate per payment period
0
Number of payments
10
Payment timing
End of period

Expected result

Present value factor
10
Future value factor
10
Worked example: Two payments in advance

Sample inputs demonstrate the method. They are not a forecast or product offer.

Interest rate per payment period
10
Number of payments
2
Payment timing
Beginning of period

Expected result

Present value factor
1.91
Future value factor
2.31

Understanding your result

Multiply a level payment by the present-value factor for its starting value, or by the future-value factor for its accumulated end value. Both assume an unchanged rate throughout the term.

The factors are mathematical multipliers, not promised returns or lifetime-annuity quotes. They contain no mortality assumptions, insurer charges or tax treatment.

Questions you might have

Can I enter an annual rate for monthly payments?

Convert it to the matching monthly rate first. This input is explicitly per payment period.

Choosing the right inputs

Interest rate per payment period
Enter the rate for one payment period. Monthly payments need a monthly rate already converted using the appropriate nominal or effective convention.
Number of payments
Enter the number of payments, not automatically years. The count and interest rate must refer to the same interval.
Payment timing
Choose end or beginning of period. Beginning payments occur one period earlier, receiving extra growth or less discounting.

Common mistakes to avoid

  • Do not enter an annual rate with a monthly payment count without first converting the rate appropriately.
  • Do not read a factor as a monetary payment amount before applying it to the relevant payment or inverse calculation.

Assumptions to check

  • Factors are mathematical multipliers, not insurance annuity prices.

Sources and method

Read our calculation and testing approach.