Mortgage calculator

A mortgage is a long-term loan secured on a property. The bank lends you most of the purchase price and you repay it in regular monthly instalments, usually over 20 to 30 years. Until the loan is cleared the property carries a charge, and if you stop paying the bank can sell it.

For most people a mortgage is the largest financial commitment of their life. That is exactly why it pays to understand how the payment is worked out: the gap between well and badly chosen terms usually runs to tens of thousands of euro.

The payment is an annuity, so it stays the same size throughout. What changes is the split inside it: at the start most goes on interest and only a little on principal, and by the end it is the other way round. The reason is simple, interest is charged on the balance, and the balance is largest at the beginning.

Picture the first payment on a €200,000 loan at 4%. For the first month the bank is owed interest on the balance: 200,000 × 0.04 / 12 = €666.67. If the payment is €1,055.67, barely €389 is left to reduce the debt. That is why the principal falls so slowly at first.

Twenty years later the balance is small and so is the interest on it and almost all of the same payment goes to the principal. That shifting ratio is what amortisation is.

The formula looks for the constant payment that leaves the debt at exactly zero after the last one. It comes from the present value of an annuity: the loan equals the sum of the discounted future payments.

The denominator 1 − (1 + i)⁻ᴺ is the annuity factor. It says what a series of N future payments of one euro each is worth today. Dividing by it spreads the loan into equal monthly amounts.

At a rate of zero the formula collapses into plain division: the payment is simply the principal divided by the number of months.

Mind the units: both the rate and the number of periods must be monthly. Putting an annual rate against a monthly count is the most common mistake when working this out by hand.

LTV (loan-to-value) is the ratio of the loan to the value of the property. Borrow €160,000 against a €200,000 flat and the LTV is 80%.

The bank cares because the property is its security. At a low LTV it has a large cushion, even if prices fell and it had to sell, it would get its money back. At a high LTV there is no such cushion, the risk is greater, and it prices that into a higher rate.

Slovakia caps LTV at 90% by law, and only a limited share of new loans may exceed 80%. In practice that means no mortgage without at least 10% of your own funds, and materially better terms from 20% up.

An overpayment goes entirely to the principal: no interest is charged on it. That lowers the balance the interest is calculated on every month after. The effect compounds: a smaller balance means less interest, so more of the regular payment goes to the principal, which shrinks the balance faster still.

On a €200,000 loan at 4% over 25 years, paying an extra €200 a month repays it six years early and saves roughly €31,000 in interest. Try it in the calculator above: the figures recalculate instantly.

Slovak law allows up to 20% of the principal to be repaid without a fee once a year, on the anniversary of the fixed-rate period. Outside that window the bank normally charges a fee, so it pays to time larger payments to it.

Every term used in this calculator has its own encyclopedia entry with a detailed explanation.