Compound interest calculator

When you leave money in a savings account, the bank adds interest to it, and the following month that interest earns interest too. This is called compound interest, and it is why money grows faster and faster. If you put £100,000 into a savings account paying 4% a year and add £2,000 every month, you will have over £440,000 after ten years, even though you have paid in only £340,000 yourself.

The calculator works the way most savings accounts do: interest is added once a month, and the monthly rate is one twelfth of the annual rate. Regular deposits are made at the end of the month, so in the month you make one it does not earn interest yet. If you do not want to make any deposits, leave the box at zero.

How it works

The calculator uses this formula:

$$K=c\cdot {(1+\frac{p}{1200})}^{12n}+m\cdot \frac{{(1+\frac{p}{1200})}^{12n}-1}{\frac{p}{1200}}$$

Here c is the starting deposit, p the annual interest rate in per cent, n the number of years and m the monthly deposit.

An annual rate of 4% is $4÷12\approx 0.333$% a month, so each month the balance is multiplied by $1+\frac{4}{1200}\approx 1.00333$. Over ten years that is 120 months. The starting deposit therefore grows to

$$\mathrm{100,000}\cdot {1.00333}^{120}\approx \mathrm{149,083.27}$$

The monthly deposits form a geometric sequence: the last deposit earns no interest at all, the one before it earns interest for one month, and the first earns interest for 119 months. We add them all up with one formula, and they come to

$$\mathrm{2,000}\cdot \frac{{1.00333}^{120}-1}{0.00333}\approx \mathrm{294,499.61}$$

In total there is £443,582.88 in the account. You have paid in 100,000 + 120 · 2,000 = 340,000, that is £340,000, so the interest comes to £103,582.88.

One thing the calculator does not do is account for tax. In the UK, interest above your personal savings allowance is taxed at your income tax rate, so the interest you actually keep may be lower. The article on monthly interest from an annual rate also shows how quickly money grows when you leave it to compound and take nothing out.