Survey of Math Chapter 21: Simple and Compound Interest
Simple Interest is interest which applies only to the principal amount.
Compound Interest is interest which applies to the accumulated amount.
Simple interest is used in some situations rather than compound interest--for example, here is a document on disability payments for British Columbia which states that the interest paid on compensation will be simple interest (see page 466 of the document (page 6 of the pdf)). This would be an example of a savings situation that uses simple interest. Also, there are some student loans that use simple interest. These would be examples of borrowing situations that use simple interest.
Another popular example of simple interest is the use of simple interest bonds. Here is a link to Canada Savings Bonds. Selling bonds allow an organization (government, church, financial institution, etc) to raise money by borrowing from the buyer of the bond, and the buyer of the bonds to have a secure way of saving money for the future.
Example
You invest $2000 in a 30 year bond with 9.5% simple interest. How much interest would the bond accumulate by the time it matures in 30 years?
Solution
If you think of this as saving, the bond over 30 years with simple interest will accumulate the amount:
A = P(1+rt) = $2000 (1+ 0.095 x 30) = $7700
The amount of interest you earn on the bond over 30 years with simple interest is:
I = Prt= $2000 x 0.095 x 30 = $5700
The bond may pay you the interest earned once a year, and after 30 years you will receive the principle, so your yearly income from the bond would be
Pr= $2000 x 0.095 = $190
If instead the bond earned compound interest of 9.5%, with interest compounded once a year, after 30 years the bond would be worth:
A = P(1+i)k = $2000(1+0.095/1)30 = $30,440.60