What is the formula for the present value of an ordinary annuity?

PV = PMT x [1 - (1+r)^(-n)] / r, where PMT is the periodic payment, r is the periodic interest rate (annual rate divided by number of periods per year), and n is the total number of periods. For an annuity-due (payments at start of period) multiply the result by (1+r).

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

An ordinary annuity makes payments at the end of each period — most mortgages, car loans and coupon bonds work this way. An annuity-due makes payments at the start of each period, which is common for rent, insurance premiums and some leases. Because an annuity-due receives each payment one period earlier, its present value is always higher by a factor of (1+r) compared with an otherwise identical ordinary annuity.

How do I use this to calculate a loan repayment?

Select "Find Payment (given Present Value)" mode, enter the loan amount as the Present Value, your annual interest rate, the term in years, and your payment frequency (usually monthly). The calculator returns the periodic payment — this is the standard amortising-loan payment formula PMT = PV x r / [1 - (1+r)^(-n)].

How do I calculate how much I need to save each month to reach a goal?

Select "Find Payment (given Future Value)" mode and enter your savings target as the Future Value. The calculator solves PMT = FV x r / [(1+r)^n - 1] (ordinary annuity) or divides by (1+r) for annuity-due, giving you the exact periodic deposit required.

What does the payment schedule show?

Each row shows the period number, the fixed payment, how much of that payment is interest (balance times the periodic rate), how much reduces the principal (or increases the savings balance), and the running balance. For a loan the balance falls to zero; for a savings annuity the balance grows to the target Future Value.

Yes. All calculations run in your browser using JavaScript. No figures are sent to a server or stored anywhere. You can use the calculator offline once the page has loaded.

Annuity Calculator — Gera Tools

An annuity is a series of equal, equally-spaced cash flows — think monthly mortgage payments, pension income, or regular savings deposits. The Annuity Calculator handles all four standard problems in time-value-of-money analysis:

Present Value (PV) — how much is a stream of future payments worth today?
Future Value (FV) — how much will a stream of regular contributions grow to?
Payment from PV — what equal payment clears a known loan balance?
Payment from FV — what regular deposit reaches a savings goal?

It supports both ordinary annuities (payments at the end of each period, as in most loans and bonds) and annuities-due (payments at the start, as in rent and insurance), at any of six payment frequencies — weekly through annual. The full period-by-period payment schedule is built on demand so you can see exactly how the balance or savings pot evolves over time.

How it works

The tool applies standard time-value-of-money formulae. Let PMT be the periodic payment, r the periodic interest rate (annual rate divided by payment frequency, divided by 100), and n the total number of periods (years times frequency):

Present value of an ordinary annuity:

PV = PMT * [1 - (1+r)^(-n)] / r

Future value of an ordinary annuity:

FV = PMT * [(1+r)^n - 1] / r

For an annuity-due, every payment arrives one period earlier, so both values are multiplied by (1+r). Rearranging either formula for PMT gives the payment needed to match a known PV (loan repayment) or FV (savings goal).

When the interest rate is zero the formulae simplify to PV = FV = PMT * n.

The schedule is built by iterating period by period: for a loan, interest accrues on the outstanding balance and the payment reduces principal; for a savings annuity, the deposit plus accrued interest compounds the growing balance. Both sequences converge to the exact analytical result within floating-point precision.

Worked example

Suppose you take out a $50,000 personal loan at 6% per year for 5 years, paid monthly (ordinary annuity). Select “Find Payment (given Present Value)”, enter $50,000, 6%, 5 years, monthly. The periodic rate is r = 6 / 100 / 12 = 0.005 and n = 60.

PMT = 50000 * 0.005 / [1 - (1.005)^(-60)]

PMT = 250 / [1 - 0.7414] = 250 / 0.2586 = $966.64

Loan	Rate	Term	Frequency	Monthly payment	Total interest
$50,000	6%	5 yr	Monthly	$966.64	$7,998
$50,000	8%	5 yr	Monthly	$1,013.82	$10,829
$50,000	6%	3 yr	Monthly	$1,521.20	$4,763
$100,000	6%	10 yr	Monthly	$1,110.21	$33,225

Now for a savings goal: you want $100,000 in 10 years at 5% annually, monthly contributions (ordinary annuity). Select “Find Payment (given Future Value)”, enter $100,000, 5%, 10 years, monthly. The result is approximately $644.13 per month, with total contributions of $77,295 and interest earned of $22,705.

Every figure is calculated in your browser — no numbers are uploaded or stored.