### 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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