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:

$1*(1+1/n)ⁿ

Where n is the number of times that interest is credited or compounded per year

a) What is the amount if interest is compounded hourly?

b)1.What is the amount if n=1,000,000,000?