Compound Interest Application

Imagine you start with $1.00 in a bank account that pays 100% interest per year. If the interest is credited once (annually) at the end of the year, the value of the account at year-end will be $2.00. If the interest is credited twice in the year (semi-annually), the interest rate for each 6 months will be 50% (100%/2), so the initial $1 is multiplied by 1.5 twice (1 to include the original principal and .5 to add 50% more), yielding $1.001.52= $2.25 at the end of the year. Compounding quarterly yields $1.001.254= $2.4414. This formula can be written as: