# About

The interest calculator is a tool to help illustrate the financial gains that can be made just with the power of compound interest and regular saving. Often times it can be confusing to understand the astronomical rates of interest that can be paid on loans and mortgages if left unpaid.

The amount of money that can be earned in a savings account or ISA with a good interest rate can also be underestimated with the impact of small interest rate increases causing a big difference in earnings.

## How it works

The interest calculator requires a minimum of 3 figures to generate a set of results from:

- An initial deposit
- Number of years saved for
- Gross interest rate

The initial deposit is taken as the first contribution to, for example, a savings account. If the interest is compounded once per year, interest is evaluated on the current total at the end of the year and before any yearly top ups.

If interest is compounded monthly, 1/12th of the interest rate is compounded every month, also before any monthly top ups. This may not be indicative of the exact top-up/compounding setup that a real savings account/investment may have so please seek advice from the institution providing the interest rate.

If a second interest rate is provided, the results will allow you to compare the different yields between the two rates.

## What is AER?

The acronym AER stands for Annual Effective Rate. APY (Annual Percentage Yield) is often used in the United States to describe the same process. This is used to show the equivalent yearly interest rate which can be used to compare between rates that compound at different intervals.

When calculating interest on a yearly basis, the formula is as follows:

**n x (1 + i)**

Where "n" can be considered the amount in savings to be compounded and "i" is the gross interest rate as a decimal. For instance with a deposit of £100 saved at 5% interest, we get **100 x 1.05 = £105**.

Things change when the interest is compounded more frequently than once a year as the amount in savings is marginally higher each time the compound happens. Take for instance an interest rate of 5% which is evaluated on a monthly basis, the formula for each compound event is:

**n x (1 + i/f)**

Where "n" is the amount in savings, "i" is the gross interest rate and "f" is the frequency of compounds per year, with monthly being a frequency of 12 per year. The savings are now multiplied by 1.004167... 12 times which evaluates as follows (figures rounded):

- 100
- 100.42
- 100.84
- 101.26
- 101.68
- 102.10
- 102.53
- 102.95
- 103.38
- 103.81
- 104.25
- 104.68
- 105.12

You can see that at the end of the 12th month, we end up with £0.12 more just by increasing the compounding frequency.

This leads us to have an AER which is the annual rate that this works out to and is calculated as follows:

**AER = (1 + i / f)**

^{f}-1With "i" being the gross interest rate as a decimal (0.05) and "f" being the frequency of compounds in a year (12).

This evaluates to 5.116% AER even though the gross interest rate was 5%. .

### Disclaimer

The results of the interest calculator are designed only for illustration purposes and does not constitute professional financial advice nor does it promise that the results are accurate for the purpose of basing financial decisions from.