Annuity payments: how to calculate a loan yourself

The bank sends a schedule: a 500,000-ruble loan for three years at 20% a year, the payment 18,582 rubles a month. The figure looks pulled out of thin air, and most people simply sign. Yet the payment follows a formula a bank analyst derives in a minute — and you can check it yourself with an ordinary calculator. Let's see what an annuity is and where that number comes from.

What an annuity is

An annuity payment means you pay the bank the same amount every month until the end of the term. The alternative is differentiated payments: the principal is repaid in equal parts, so the payment gradually shrinks. Retail banks almost always offer an annuity: a flat amount is easy to remember and build into a budget, and it makes the bank's cash flow easier to plan.

To be fair: the total interest paid is usually lower with differentiated payments — the principal shrinks faster, so interest accrues on a smaller balance. But the early payments there are noticeably heavier, and qualifying takes a higher verified income. Choosing an annuity isn't always a rip-off; often it's a deliberate trade-off between convenience and total cost.

Annuities also have a non-obvious side: the payment stays the same, but its composition keeps changing. In the first months most of it goes to interest, and only a small part to the principal itself. That's no conspiracy, just arithmetic: interest accrues on the outstanding balance, and early on the balance is at its maximum. Hence the familiar effect — after a year of payments, the principal has shrunk noticeably less than what you've paid.

The formula, in plain language

The formula itself looks scary, but its logic is transparent. Here's the sequence:

1. divide the annual rate by 12 to get the monthly one: 20% a year is 1.667% a month, i.e. 0.01667;
2. raise one plus the monthly rate to the power n, where n is the number of payments: for three years, n = 36;
3. multiply the monthly rate by that number and divide by the same number minus one — that gives the annuity factor;
4. multiply the loan amount by the factor — that's the monthly payment.

For the loan in the example above, the factor comes out to about 0.03716; multiply by 500,000 and you get 18,582 rubles a month. Over three years you'll pay back about 669,000 rubles, of which about 169,000 is interest. Check the math on your own numbers in the loan calculator: it builds the schedule instantly and shows how the debt is paid down.

Payment: 18,582 ₽ every month, all 36 times
First payment: 8,333 ₽ interest + 10,250 ₽ principal
Last payment: about 300 ₽ interest + 18,280 ₽ principal

Notice how the composition shifts: in the first payment nearly half is interest; in the last, interest is one and a half percent. The interest share “squeezes” as the balance shrinks — the principal picks up the pace toward the end of the term all by itself, with no extra payments.

What to check before signing

• the total cost of the loan, not just the rate: it includes insurance and fees, and the lender must show it in a framed box on the first page of the contract;
• how early repayment is recalculated: shortening the term wins on total interest, lowering the payment wins on monthly strain on the budget;
• insurance: what's included, what it costs, and whether you can refuse it during the “cooling-off period” after the loan is issued;
• the actual disbursement and first-payment dates: interest for a partial month is counted by days, so the first payment may differ from the scheduled one;
• the schedule itself: the bank must attach it, and it shows at a glance how much of each payment goes to interest.

One general note: any promises a manager makes — “we'll lower the rate if you refinance,” “the insurance will be refunded later” — only count if they're written into the contract. A payment schedule won't back up a verbal assurance.

An annuity isn't a bank trick; it's a way of splitting a debt into equal parts in which interest always goes first. It's worth understanding this before signing, not after: knowing the formula, you'll check the schedule calmly, compare two offers, and won't be surprised by the slow decline of the debt in the first year. Ten minutes with a calculator before the bank visit is the best-performing investment in the whole contract.