 
Interest is the price you pay to borrow money, or the return earned on an investment or bank account. Interest is often reflected as an annual percentage of the amount of a loan or deposit. This percentage is known as the interest rate. Compound interest is the interest you earn on the interest you've earned, as well as on the original amount invested. On these pages we'll explain both, with lots of examples. Let's start with a simple example, appropriately called 'simple interest'. Example 1: Suppose you have a bank savings account with $100 in it. This is called the principal. It's called a savings account because the bank pays you interest for leaving your money in the account. In this example, we'll make the annual interest rate 1.5%. This means that after a year is passed, the bank will gift you with 1.5% of the principal. How much is this? 1.5% of $100 = 0.015 x 100 = $1.50 Your investment has earned $1.50 after one year. This is called simple interest because you take out the $1.50 and spend it, so that in the second year, you are once again getting interest on just the principal of $100. You can of course add money to your account to increaase the principal, which will result in more interest. The point here is that, for simple interest, you always take out the interest payments, so that the bank won't be paying you interest on that interest, as well as on the principal. Example 2: Deposit a principal of $2500 in an account that pays an annual 0.5% rate of interest. Interest earned after 1 year = 0.5% x Principal I = 0.5% x $2500 = 0.005 x 2500 = $12.50 Let's make a formula: Using I for interest earned, r for the annual interest rate, and P for the principal: I = r · P Let's use this formula in a third example: Example 3: Deposit $800 at an annual rate of 2% I = r · P = 2% x $800 = 0.02 x 800 = $16. Suppose you don't leave your money in the account for the full year, but remove it after a fraction of a year. How much interest would you get? Example 4: You leave a deposit of $2000 in the bank for 3 months at an annual rate of 1%. How much interest will you get? Clearly you'll only get interest for a fraction of a year. The fraction of a year is 3/12, or 1/4, or 0.25 I = 3/12 of 1% of $2000 I = 0.25 x 0.01 x 2000 I = $5. The total amount you will have will be the principal plus the interest: A = P + I A = $2000 + $5 A = $2005 Example 5: You deposit $1500 at an annual rate of 3% and leave it for 5 years, removing the interest each year. How much interest in total will you have earned? I = 5 x 3% x $1500 I = 5 x 0.03 x 1500 I = $225 Example 6: After 112 days, you withdraw your principal of $8000 which was earning an annual rate of 1.5%. What interest will you have made, and what total amount will you have? I = 112/365 of 1.5% of $8000 I = 112/365 x 0.015 x $8000 I = $36.82 A = $8036.32
Example 7: $4000 is deposited for 18 months at an annual rate of 2%. Find the interest earned. I = t · r · P I = 18/12 x 2% x $4000 I = 1.5 x 0.02 x 4000 I = $120 Let's move on and look at compound interest ... |