### Compounded Interest (Future Value)

Compound interest is when interest is immediately re-invested.

This is an example of a __Geometric Sequence__ where a series of numbers are multipled by a fixed amount.

**Annual Compounding**

If you invested £50 today how much would you have **after 3 years** if the interest rate is 6% with annual compounding?

If you invested £50 today how much would you have **after 185 days** if the interest rate is 6% with annual compounding?

**Semi-Annual Compounding**

If you invested £50 today how much would you have after 3 years if the interest rate is 6% with semi-annual compounding?

Semi-annual compounding means that the interest is calculated and re-invested every 6 months.

**Quarterly Compounding**

If you invested £50 today how much would you have after 3 years if the interest rate is 6% with quarterly compounding?

**Monthly Compounding**

If you invested £50 today how much would you have after 3 years if the interest rate is 6% with monthly compounding?

**Daily Compounding**

If you invested £50 today how much would you have after 3 years if the interest rate is 6% with daily compounding?

**Important**

The higher the interest rate the larger the future value

The shorter the compounding period, the larger the future value.

It is common to compute the future value of $1, then multiply it by the original amount.

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