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Annuity Due Calculator

Value an annuity due where payments come first.

How it is calculated

The tool converts the yearly inputs to per-period ones, i = annual rate ÷ 100 ÷ payments per year and n = years × payments per year, then discounts the payments with the beginning-of-period adjustment: PV = payment × (1 − (1 + i)−n) ÷ i × (1 + i). Payment is the amount of each instalment in dollars, annual rate is the nominal yearly rate in percent, and compounding matches the payment frequency (12 for monthly, 4 for quarterly, 1 for yearly). With a rate of 0 the present value is just payment × n. The tool also reports the plain sum of all payments, so the gap between the two figures is the effect of discounting. Years must be above zero and payments per year a whole number above zero. A negative payment, a rate of −100% or lower, or empty fields give no result.

Worked example

Rent of $1,200 is paid at the start of every month for 5 years, discounted at 6% a year. Monthly rate: 6 ÷ 100 ÷ 12 = 0.005; periods: 5 × 12 = 60. Ordinary annuity factor: (1 − 1.005−60) ÷ 0.005 ≈ 51.7256, so 1,200 × 51.7256 ≈ 62,070.67. Moving every payment to the start of the period multiplies by 1.005, giving $62,381.03. The undiscounted total of the payments is $72,000.00.

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Common mistakes

  • Entering the monthly rate as the annual rate. The rate field is the yearly rate; the tool divides it by the payments per year itself.
  • Setting payments per year to 1 for monthly payments. The frequency must match how often the payment is made, or both the rate and the number of periods are wrong.
  • Typing a fractional frequency such as 2.5 payments per year, or a negative payment to represent money paid out. Both give no result; enter a whole number and a positive amount.
  • Using this tool for payments made at the end of each period. Those need the ordinary-annuity value, which here would be lower by the factor 1.005 at these inputs.
  • Reading the present value as what you will receive in total. The total of the payments is shown separately; the present value is smaller because later payments are discounted.

Sources

About this calculator

An annuity due is a series of equal payments made at the beginning of each period rather than at the end, which is the defining difference from an ordinary annuity. Because each payment is received or paid one period earlier, it has more time to earn interest (or costs more to fund), so its present value is higher than an equivalent ordinary annuity by a factor of (1 + r). The formula is PV = PMT × [(1 − (1 + r)^−n) / r] × (1 + r), where PMT is the payment, r is the interest rate per period, and n is the number of periods.

Annuity-due timing shows up in real financial products more often than people expect: rent is typically paid at the start of the month, insurance premiums are often billed in advance, and many lease agreements require the first payment upfront. Because each payment arrives at the start of its period, it values the stream from your payment, rate and number of periods with annuity-due timing, which avoids the undervaluation an ordinary-annuity formula would give.

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