Learning about Investments in L214

ever wonder where the equation pt=p0(1+r)^t came from?

 try solving this problem: I have $5500in my account and it increases by 2% each year, whats the balance after 3years?  4?5?

1st year: 5500+(2%x5500) = $5610 *so i have $5610after1 year
2nd year: 5500+(2%x5500)+[2%(5500+2%x5500)]=$5722.20 so i have 5722.2for the 2nd year.
3rd year: etc.
if you simplify the 2nd year's equation, you'd find 5500+(2%x5500)+[2%(5500+2%x5500)] is equal to 5500(1+2%)^2
2nd year-to the 2nd power
3rd year-to the 3rd power
4 year- to the 4th power
t year- to the t power.
➸and thus the equation   p(t)=p0(1+r)^t
:)