What is the difference between an ordinary annuity and an annuity-due?

Timing. An ordinary annuity pays at the end of each period (loans, bonds); an annuity-due pays at the beginning (rent, leases, many insurance premiums). For the same present value, annuity-due payments are smaller because each is invested or owed one period earlier.

How do I set the rate per period?

Divide the annual rate by the number of payments per year. For monthly payments at 6% annual, use 0.5% per period and set the period count in months. The rate and the count must use the same time unit.

Can I use this for a mortgage payment?

Yes. Enter the loan amount as the present value, the monthly rate (annual ÷ 12), and the number of months (years × 12). The ordinary-annuity payment is your monthly principal-and-interest amount.

What if the interest rate is zero?

With no interest, the payment is simply the present value divided by the number of periods — you repay the principal in equal installments. The calculator handles this case directly.

Does total interest depend on the annuity type?

Yes, slightly. Because annuity-due payments are smaller per period but made earlier, the total paid and total interest differ marginally from an ordinary annuity for the same present value, rate, and term.

What is the difference between an ordinary annuity and an annuity-due?

Timing. An ordinary annuity pays at the end of each period (loans, bonds); an annuity-due pays at the beginning (rent, leases, many insurance premiums). For the same present value, annuity-due payments are smaller because each is invested or owed one period earlier.

How do I set the rate per period?

Divide the annual rate by the number of payments per year. For monthly payments at 6% annual, use 0.5% per period and set the period count in months. The rate and the count must use the same time unit.

Can I use this for a mortgage payment?

Yes. Enter the loan amount as the present value, the monthly rate (annual ÷ 12), and the number of months (years × 12). The ordinary-annuity payment is your monthly principal-and-interest amount.

What if the interest rate is zero?

With no interest, the payment is simply the present value divided by the number of periods — you repay the principal in equal installments. The calculator handles this case directly.

Does total interest depend on the annuity type?

Yes, slightly. Because annuity-due payments are smaller per period but made earlier, the total paid and total interest differ marginally from an ordinary annuity for the same present value, rate, and term.

Annuity Payment Calculator

Find the periodic payment of an annuity from its present value, interest rate, and number of periods — for both ordinary annuities and annuities-due.

Result

Payment per period (ordinary)

$599.55

360 payments · total $215,838.19

Payment per period$599.55
Number of payments360
Total of payments$215,838.19
Total interest$115,838.19
Ordinary-annuity payment$599.55
Annuity-due payment$596.57

Source: Ordinary annuity payment: PMT = PV·r / (1 − (1+r)^−n). Annuity-due divides this by (1+r).

Not financial advice — The rate must be per period and match the period count (monthly rate with monthly periods). Annuity-due payments are slightly smaller because each payment is made earlier and earns interest longer.

Step-by-step

Ordinary payment = PV·r ÷ (1 − (1+r)^−n) = $100,000.00×0.005 ÷ (1 − (1+0.005)^−360) = $599.55.
Ordinary annuity pays at period end: $599.55.
Over 360 periods you pay $215,838.19, of which $115,838.19 is interest.

How to use this calculator

Enter the present value (the loan or lump sum today).
Enter the interest rate per period — divide an annual rate by the payments per year.
Enter the total number of payments.
Choose ordinary or annuity-due and read the payment amount.

About this calculator

An annuity is a series of equal payments made at regular intervals — a mortgage, car loan, or retirement payout, for example. This calculator solves for the payment amount that exactly pays off (or pays out) a given present value over a set number of periods at a fixed interest rate. It uses the standard time-value-of-money formula, where the present value equals the payment times the present-value annuity factor. The key distinction is timing: an ordinary annuity makes each payment at the end of the period (typical for loans), while an annuity-due makes each payment at the beginning (typical for rent or insurance premiums). Because annuity-due payments arrive earlier and earn interest one extra period, they are slightly smaller for the same present value. Be sure your interest rate and period count use the same time unit — a monthly rate with a monthly count.

How it works — the formula

Ordinary:     PMT = PV · r / (1 − (1 + r)^−n)
Annuity-due:  PMT = Ordinary / (1 + r)
(r = rate per period, n = number of periods)

The present value equals the payment times the annuity present-value factor; solving for the payment inverts that. Annuity-due shifts each payment one period earlier, scaling by 1/(1+r).

Source: Investopedia — Annuity

Worked examples

Example 1

PV $100k, 0.5%/mo, 360 mo (6% / 30 yr)

Inputs:: pv=100000, rate=0.5, periods=360, type=ordinary
Output:: $599.55/month

Example 2

PV $20k, 0.5%/mo, 60 mo

Inputs:: pv=20000, rate=0.5, periods=60, type=ordinary
Output:: $386.66/month

Example 3

Same as #1 but annuity-due

Inputs:: pv=100000, rate=0.5, periods=360, type=due
Output:: $596.57/month

Limitations

Fixed rate and equal payments assumed.
Rate and period count must share the same time unit.
Ignores fees, taxes, and any balloon or irregular payments.

Time-value-of-money calculation; confirm exact loan terms with your lender.

Frequently asked

For an ordinary annuity, PMT = PV × r ÷ (1 − (1 + r)^−n), where r is the rate per period and n is the number of periods. This is the same formula behind a fixed mortgage or loan payment.