From: Michele

Currently there is $10,000 in a customer's savings account that earns 4% interest compounded annually.
How much interest will the customer earn in a year?

Hi Michele.

This simple answer to your question is 4% of $10 000. Here's why:

In general, compound interest just means that interest is paid on the total amount the customer has accumulated by the time the interest is to be paid. This is not the same as simple interest which only pays interest on the principal.

Compound Interest Formula:
There is a general formula for compound interest that looks something like this:

a = P (1 + R/n)ny

In this formula, a =accumulated value
P =principal
R =annual interest rate
n =number of times per year that interest is paid out
y =number of years

In your question, the annual interest rate is 4% (R = 4%), you want to know what happens after 1 year (y = 1), the interest is paid out annually (n = 1), and the principal (that's the initial amount invested) is $10 000 (P = $10 000). So in your case, the equation is this:

a = $10 000 (1 + 4%/1)1*1 = $10 000 (1 + 4%)

Can you see from this that the amount accumulated is just $10 000 (the original principal) plus 4% of $10 000 (the interest)?

More complicated questions will have other values, so you could be asked the question "If I invest $550 and the interest rate is 3% per year, compounded monthly, then how much will I have after two years?" Using the information above, you should know how to solve this question.

Hope this helps!
Stephen La Rocque.