There are all kinds of fancy interest rate calculations, but the only ones you probably need to know are the Annual Percentage Rate (APR) and the Annual Percentage Yield (APY).
The APY relates to the rate banks pay you when they ‘borrow’ your money. (Yes, whenever you deposit money in a checking or savings account, you are loaning them money).
The APR relates to the rate you pay when you borrow money from a lender.
The difference between the interest rate you loan money to the bank and the interest rate the bank loans money to you is the interest rate margin, which is how the banks make their money (along with fees and investments).
Let’s talk about the APY first. Remember the A in APY stands for Annual. The bank is agreeing to pay you a certain interest rate over the over the course of a year.
So if you leave our $20,000 in your account for a year without touching it, and receive an APY of 4%, you simply multiply the $20,000 by 4% = $800.00. At the end of the year you have $20,800.
From the example above, $800 is your total for 1 year at 4%. But how much are you earning each day? Well, there are 365 days in a year, so you take $800/365 = 2.19. You will roughly get $2.19 interest per day.
What about 1 month? There are 12 months in a year. So 800/12=66.67. Each month, you will earn $66.67 more in interest.
In reality it can get a little more complicated. You will often read the following on an interest rate agreement: "interest rate is listed on an annual basis, accrued daily, and paid monthly".
Interest rate is listed on an annual basis
As we saw, the 4% interest you see is for a year. If you take your $20000 out of the bank in 6 months, you will not see $800 in interest. You will see less, about $400, assuming there is no penalty.
This also means each day the bank calculates your interest earnings for that day. The first day you put your money in the bank account, you earned $2.19 interest. Leave it another day, and you earn another $2.19.
At the end of the month, the bank will pay you the interest you've accumulated for that month. For the first month, lets say there are 31 days. You earned $67.95 in interest. Your bank will add this amount to your current $20,000 balance. So you will now have $20,067.95.
The next day, your bank will start accruing your interest earned again. This time, the bank will calculate your interest based on the new balance of $20,067.95. The amount of interest earned is added to your original balance, which will in turn earn interest for you. This is called compound interest.
Suppose you deposit $1000 in a bank account that pays five percent interest annually. At the end of one year, your balance will have grown by $50 (that's five percent of your starting thousand) to $1050. Assuming you leave the entire $1050 in your account, the interest you get during the next year will be greater - five percent of the entire $1050. You make no further contributions; you just leave your money alone and let compound interest work its magic. Overtime the principal grows exponentially.