There are several terms that must be understood before using the formula.
The principal which is the money that is being invested known from now on as P.
The no of years that the investment will earn interest known from now on as Y
The interest rate known from now on as I
The simple interest
The simple interest means that interest will be earned yearly on the same amount.It also mean that you will not allow interest to accrue on the interest. You will probably remove it for spending.
It is calculates as follows.
Interest yearly = P x I/100
Total interest after Y years = P x (I/100) x Y
eg $10000 invested at 10 % for five years.
Interest every year = P x I = 10000 x (10 /100) = 10000 x 0.1 = 1000
Interest after five years = P x I x Y = 10000 x (10 /100) x 5 = 10000 x 0.1 x 5 = 5000
Amount after five years = $ 15000
If you are having problems with the mathematics, I have created a calculator to determine the simple interest here.
The compound interest
In compound interest the calculation is a little bit different. Each yearly interest is added to the principle to calculate the following year's interest. As a result with time the principal increases and the the interest increases. Provided you don't use the yearly interest.
Lets say $ 100000 is invested at an interest rate of 10 % for five years
After one year the interest obtained = 10000 x 0.1 = 1000
On the second year the interest obtained = (10000 +1000)x 0.1 = 1100
As you can see $ 100 dollar is obtained more than the first year. This will continue to increase for each year. More interest is obtained. However if you use the interest it would be a simple interest. The key is to leave the interest untouched.
Now this is a little bit difficult if the investment will last over several years. Here is general formula.
Lets say $ 10000 is invested at an interest rate of 10 % for five years.
I = 10 % = 10/100 = 0.1
i = 0.1+1 =1.1
The total amount after five years = P x i x i x i x i x i = P x i ^ Y = 10000 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 = 16105
As you can see compared to the simple interest $1600 dollars more is obtained. When a compound interest system is obtained the gain over the long term is more than the simple interest system.
If you are having problems with the maths. I have created a calculator to determine the compound interest here.
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Simple and compound interest
How to calculate compound interest on an investment