# Activity: Calculating Interest

There are a few things our children should know how to do before they leave home.  One of these is to know how to calculate interest.

Back in the day (way back) calculating interest was incorporated into math books in such a way that the eighth-grade graduate had a firm handle on the subject.  Several years ago, one of the classes you ended up taking in college included several weeks spent on calculating simple interest.  College!  We can do better….

There are several reasons why it is important for our children to understand this subject:

1. As they work to establish their credit, they will be confronted with very “helpful” credit card companies willing to loan them money.  They need to understand how much what they buy really costs.
2. Hopefully, when they begin earning their way they will be putting something aside.  They need to understand how much a small, safe investment earning only 1% interest will be worth in just 10 short years!
3. Understanding interest will help them understand the effect inflation can have on their earnings.

Calculating interest isn’t that hard to understand. For simple interest:

I=P*r*t

Where I is the interest earned, P is the principal or amount invested, r is the interest rate, and t is the time of investment in years.

Example:

The simple interest earned on \$400 invested at an interest rate of 4% per year over 3 years is

I = \$400 * 0.04 * 3

or \$48.

Compound interest is simply interest money earning interest, so that when interest is calculated on the initial principal amount it is also calculated on the amount of interest already accumulated — compounding the interest.  For compound interest:

V= P * (1 + r/n) nt

Where V is the future value, P is the principal or amount invested, r is the interest rate, n is the number of times the interest is compounded in 1 year, and t is the number of years.  This formula is reduces to V=P*(1+r)t when the interest is compounded annually, since n is 1.

Example:

The value of \$400 invested at an interest rate of 4% per year over 3 years that compounds monthly is

V = \$400 * (1 + 0.04/12) 12 * 3

or \$450.91 (the compound interest earned is \$50.91).

##### Suggestions
• Borrow from your children a small amount — perhaps from their allowance dollars, savings money, or gift cash.  Pay them back with interest over an agreed-upon time.  Have them keep a chart to see how much they are earning on their dollars.
• The next time your child asks for something — without having the cash on hand — provide him with a loan.  Help him see how much the item really ends up costing.  (Goes without saying, it will need to be a wise purchase, and he should understand up front that he is going to pay more for the item than he would if he simply waited until he had the dollars!)
• Determine how much an item would have cost 30 years ago, 50 years ago, and 100 years ago.  Compare that to today’s prices.  Help your child to see that money saved for the future will need to cover the costs of inflation.
• Look up wage tables for 30, 50, or 100 years ago.  Then look up the cost of a simple product such as milk, bread, or an automobile.  Determine the percent of the annual (or weekly) wage that would have been necessary to pay for the item.  Compare those numbers with today’s figures.
• Have your child invest his money in a CD or other safe, parent-approved vehicle.  Ask him to calculate the money he will end up with at the time of maturity.
• Look up the current interest rate on a popular credit card.  Have your child make a pretend purchase with the card. Assume he does not pay off the full amount when the credit card is due.  Make a chart showing how much is still owed after his monthly payment.  Do this same thing to show a full year.  How much is the object costing at this point?  Continue for a second year.  How much is the item costing at this point?

Interest
Includes an excellent explanation of how simple interest works (scroll down).

Compound Interest
An excellent explanation of how the formula is derived, which makes it easier to understand.

Credit Card Facts

Then and Now Prices
Chart helpful for seeing how much an average wage can buy now vs. during the Depression.

Seven Ways to Compute the Relative Value of a U.S. Dollar Amount – 1774 to Present

Annual Wages

##### Activities

Simple Interest Game
Once your children understand how to calculate simple interest, have them practice with this interactive game.

Interest Calculator
Enter an amount of deposit, annual interest rate, and number of years in the bank and the calculator will show you how much interest you earned and the total amount your money is now worth.

The Compounding Calculator
Interactive calculator that demonstrates how much a small investment can be worth in ten short years.

Debt Calculator
A great interactive way to show how much something purchased on a credit card really ends up costing.

What’s the Real Cost of Credit
Another credit card simulator geared toward teens.

Simulation of Credit Card Interest
By changing the amount and monthly payment, you can see at a glance how long it will take to pay off your credit card.

Inflation Calculator
Discover the purchasing power of a dollar over time.

##### Units & Lesson Plans

When Gas Was a Dollar
Uses a story to explain the inflation.  Use this inflation calculator.