Name: Gina
Who is asking: Teacher
Level: Secondary

Question: I'm tutoring an Algebra II student and we're having trouble with this one:

You deposit $1500 in an account that pays 6.5% annual interest, compounded continuously. Find the balance after 10 years.

I'm not sure what to do with the "compounded continuously" part.

Hi Gina,

If you invest $A at an interest rate of r for t years, compounded n times per year then the balance after the t years is

With the example that you give the balance after 10 years would be

It's an interesting calculator exercise to see what happens as you increase n. For simple interest n = 1, or you might compount twice per year (n = 2) or every day (n = 365) or every minute (n = 365x24x60) or ... What you will find is that as n increases the balance approaches $2873.3099872... This is the balance that results from "compounding continuously".

The expression that returns this balance immediately is

where e is the base for the natural logarithms (e is approximately 2.71828)

I hope this helps,
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