Money and Finance
Money and Finance
Interest
What is interest?
Interest is what it costs to borrow money for a certain amount of time. If you borrow money from the bank, then you pay the bank interest. If the bank borrows money from you, then they pay you interest.
The Interest Rate
The interest rate is the amount charged for borrowing money. It is a percentage of the total money borrowed over the amount of time. For example, the interest rate might be 2% per year on $100. In this case, the interest that would be paid for one year would be $2.
Calculate Simple Interest
The most basic type of interest is simple interest. This where the interest is only based on the initial amount of the loan called the principal. There is no interest paid on past interest earned like with compound interest (explained below).
The formula for simple interest is:
Simple Interest = Principal x Interest Rate x Length of the Loan in Time
This can be written as:
I = P x r x t
where I = Interest, P = principal, r = interest rate, t = time
Compound Interest
Compound interest is more complicated. This is where you earn or pay interest on interest previously earned. For example, if you had $100 that earned 10% interest at the end of the first year you would have $110. Then, during the second year you would earn 10% of $110 which is $11. The total interest for two years would be $21. With simple interest you would not get the extra $1 in the second year. You would only earn $10 per year and the total for 2 years would be $20.
Interest can compound at different intervals. In the above example, the interest was compounded every year. In many cases, such as with a mortgage loan from the bank, interest compounds monthly.
The formula for compound interest is:
Future Value = P x (1 + r⁄ n)nt
where P = principal, r = interest rate, t = time in years, n = number of times per year interest is compounded
This will give you the "future value" of your deposit. To figure out how much interest you earned, subtract the initial value of the deposit (P) and you will have just the interest:
Compound Interest = Future Value - P
Example Problem
Now we will do an example problem calculating both simple interest and compound interest.
How much interest would you earn if you had $50,000 in the bank for 10 years at a rate of 2%. First calculate simple interest then compound interest where the interest compounds each month.
To calculate the simple interest we use the formula:
I = P x r x t
I = $50,000 x .02 x 10
I = $10,000
To calculate the compound interest we use the formula:
Compound Interest = P x (1 +r⁄ n)nt
FV = $50,000 x (1+ .02⁄ 12)12x10
FV = $61, 059.97
Now I need to subtract the principal to get the compound interest earned:
I = $61, 059.97 - $50,000
I = $11, 059.97
You can see the additional gain when compounding interest monthly vs. simple interest.
Why do interest rates change?
Interest rates don't stay the same. There are many factors that can change the current interest rate. Like many things, interest rates can change with supply and demand. The more money there is available for loan, the lower the interest rate will be. If demand for money goes up, then so will interest rates. Government money policy has a huge influence on the interest rate because it determines the money supply. Long term interest rates are influenced by the rate of inflation.
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Note: This information is not to be used for individual legal, tax, or investment advice. You should always contact a professional financial or tax advisor before making financial decisions.
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