Compounding Interest

3.3.23 Introduction to Compound Interest

​Ana is opening a new bank account with an amazing interest rate!

She deposits $100 and will earn 12% interest each year.

​Situation

Math Response

Her interest is compounded (calculated and paid out) at the end of each year. How much money will she have after 1 year?

Type answer here

Correct Answer: 112

Deg^°

Rad

The last slide was an example of interest compounded annually – meaning Ana earns 12% interest once a year.

Compounded Annually

​But real interest is compounded more than once a year! For example, compounding "semi-annually" would mean Ana could earn 6% twice a year.

Compounded Semi-Annually

Math Response

Calculate the amount Ana would have after a year if her interest were compounded semi-annually. (You need to multiply twice!)

Type answer here

Correct Answer: 112.36

Deg^°

Rad

Open Ended

If Ana has a choice between having interest compounded annually or semi-annually, which should she choose?

Multiple Choice

Interest can also be compounded quarterly (meaning 4 times a year). If Ana's yearly interest is 12%, how much interest will she earn each quarter?

• 2%

• 3%

• 4%

• 48%

Math Response

How much will Ana have after a year if her interest is compounded quarterly? Round to the nearest hundredth.

Type answer here

Correct Answer: 112.55

Deg^°

Rad

• Most often, banks compound interest monthly (12 times a year).

• This means that Ana would earn 1% interest each month.
  

• After a year, her account would go up by a factor of (1.01)¹²

Compounding Monthly

Math Response

Calculate how much money Ana would have after 1 year if the interest were compounded monthly.

Type answer here

Correct Answer: 112.68

Deg^°

Rad

Open Ended

Ana notices that the more times interest is compounded, the more money she earns. Why do you think this is true?