Investing $1,000 at 2% annual interest compounded monthly for 3 years will earn you $8.37 more than investing the same amount at 2% annual interest compounded semi-annually for 3 years.
Here's the breakdown:
Monthly compounding:
Interest per month = (2% annual interest) / 12 months = 0.1667%
Amount after 3 years = $1,000 * (1 + 0.001667)^36 = $1,025.34
Interest earned = $1,025.34 - $1,000 = $25.34
Semiannual compounding:
Interest per period = (2% annual interest) / 2 periods = 1%
Amount after 3 years = $1,000 * (1 + 0.01)^6 = $1,016.97
Interest earned = $1,016.97 - $1,000 = $16.97
Therefore, the difference in earnings between monthly and semi-annual compounding is $25.34 - $16.97 = $8.37.
The more frequent the compounding, the faster your money grows due to the "interest on interest" effect.