The formula that gives the balance A of an account earning compound interest is A=P( 1+r )^n, where P is the principal, r is the interest rate for each compounding, and n is the number of time periods.
$ 46.54
Practice makes perfect
Compound interest is interest paid on both the original principal — the amount of money at the start — and on interest already earned. Let's recall the formula that gives the balance A of an account earning compound interest.
A= P( 1+ r )^n
In this formula, P is the principal, r is the interest rate for each compounding period written in decimal form, and n is the number of time periods. Let's carefully consider the given exercise.
Determine the compound interest earned on $ 220 invested at 3.25 % compounded annually for 6 years.
We can immediately identify P as 220. The interest rate, written as a decimal number, is 0.0325. Finally, since the interest is compounded annually, we have that n= 6. Let's substitute these values into the formula and simplify.
We found that the total returned amount of the investment with compound interest is about $ 266.54. If we subtract the original principle from this value, we will get the compound interest earned. Let's do it!
$ 266.54- $ 220=$ 46.54
The compound interest earned is $ 46.54.
