Monthly installment for buying a house

📖 The story

The Miller family finances $360,000 for their home at a 3.8 % nominal rate and chooses an initial repayment of 2 %. They want to know the monthly installment.

ℹ Annuity from the interest rate plus repayment rate.

Change any number and press "Calculate" – or use "Type in" on the right to watch it entered.

What you learn

A higher repayment rate raises the installment but shortens the term enormously. At only 1–2 % initial repayment the payoff drags on for decades – those who can, repay faster.

In short: The initial installment follows directly from the interest and repayment rates – a higher repayment rate raises the installment but shortens the term.

Formula

R = D · (p + t) / (100 · m)

With the example numbers

R = 360.000,00 € · (3,80 + 2,00) / (100 · 12) = 1.740,00 €

How to read the formula

R = D·(p+t)/(100·m) is the initial annuity from the nominal rate p plus initial repayment t. The installment stays constant, but its inner makeup shifts: with each payment the interest portion falls and the repayment portion rises – which is why repayment accelerates over time.

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