Compound Interest

​COMPOUND INTEREST

​by Miss Borchard

Compound Interest

by Marcie Borchard

​What type of a graph is this?

​The ANNUAL INTEREST RATE is important but even more important is HOW the interest is computed.

​Last week we looked at simple interest, this week we will look at COMPOUND INTEREST. Interest can be compounded:

​Annual compounding - once a year

​Semiannual compounding - twice a year or every six months

​Quarterly compounding - 4 times a year or every 3 months

​Daily compounding - every day or 365 days a year which is the most common form

​Even though they compound it every day, it doesn't add interest every day. They keep a record of interest earned and add it into the account monthly or quarterly. This is called CREDITING an account. Compounding daily and crediting monthly is the most common procedure used by banks today.

​How much interest would $1000 earn in one year at a rate of 6% compounded yearly? What would the new balance be?

​Since it is compounded yearly we use the same formula as the Simple Interest formula.

​r = 6% = .06

​I = 1000 (.06) (1) = 60

​It would earn $60 and have $1060 at the end of the year.

Open Ended

How much would x dollars earn in one year at the rate of 4.4% compounded yearly?

​I = .044x dollars

​Lily deposits $1000 in a savings account that pays 6% interest compounded semiannually. What is her balance after 1 year?

​Here is where we have a difference. Using I = prt

​1000(.06)(1/2) = 30 so the new balance is $1030

​So now the 2nd time it is compounded we have

​1030(.06)(1/2) = 30.90 so the balance is now $1060.90

​Maybe 90 cents is not a big deal but if you remember the graph at the beginning, it is not linear growth... it is exponential growth.  Little by little those few cents begin to become a few dollars and so on and so on.  Growth on growth on growth.

Open Ended

You try one.

Maddy deposits $4000 in a savings account that pays 5% interest compounded semiannually. What is her balance after 1 year?

Did you get $4202.50?​

​Try the CHECK YOUR UNDERSTANDING problem at the bottom of page 140.

​You should get $976.37