Our next exponential application is compound interest. If you invest money at an annual interest rate your money will grow exponentially by the formula:
where B is the final Balance
P is the starting balance
r is the annual interest rate (don't forget to divide a percent by 100)
n is the number of times you earn interest each year
t is the number of years the money is invested
So, if you invest $100 at 8% annual interest compounded monthly for 50 years you will have:
We played around with different amounts of compounding and found that the more compoundings per year the more money you earn, but that the increase gets smaller and smaller with large values for n.
Now that we've played with interest a bit, I want to know how long it will take to double an investment at different interest rates. To simplify, take an initial investment of $100. Working with a monthly compounding and with different interest rates, how long will it take to double the money to $200? Work it out with at least five different interest rates. See if you can come up with a rough rule for how long it will take for a different interest rate.