Simple and Compound Interest

Lesson 7-8

Simple and Compound Interest

Interest is a term used in banking. When you deposit money (put money in the bank), the bank pays you for the use of your money. The money the bank pays you is called interest.

Simple Interest

The formula used to calculate simple interest is: I = prt

Where I = interest earned

p = principal (the amount of money you put in the bank.)

r = rate (the percentage rate that the bank pays you.)

t = time (in years)

Simple interest--example

Let’s suppose you have $400 to put in a savings account. The interest rate is 5% per year, and you keep the money in the bank for 6 years.

I = prt p = 400

r = 5% or 0.05

t = 6

Substitute these numbers into the formula

I = prt I = 400 (0.05) (6) = 120

Simple interest--example

What we found is that the interest earned is $120.

What about the $400 you started with?

Simple interest--example

What we found is that the interest earned is $120.

What about the $400 you started with?

It’s still there, but now you have an additional $120 for a total of $520

Try this

Find the simple interest:

Principal = $250

Interest rate = 4%

Time = 3 years

Find the total amount after 3 years

Try this

Find the simple interest:

Principal = $250

Interest rate = 4% $30

Time = 3 years

Find the total amount after 3 years

Try this

Find the simple interest:

Principal = $250

Interest rate = 4% $30

Time = 3 years

Find the total amount after 3 years $280

Try This too

Principal = $250

Interest rate = 3.5%

Time = 6 months (be careful with this)

Find the interest:

Find the total amount after 6 months:

Try This too

Principal = $250

Interest rate = 3.5%

Time = 6 months (be careful with this)

Find the interest: $4.38

Find the total amount after 6 months:

Try This too

Principal = $250

Interest rate = 3.5%

Time = 6 months (be careful with this)

Find the interest: $4.38

Find the total amount after 6 months:

$254.38

More examples

The formula can be used to calculate other interest-related problems as well. Suppose you have $1000 to save and you know the interest rate is 5%. If you want to make $200 in interest, how long (how much time) will you need to keep the money in the bank?

More examples, cont.

We know: P = $1000 r = 5% (0.05) I = $200 Substitute these values into the formula and then

solve: I = prt 200 = 1000 (0.05) t 200 = 50t 50 50

4 = tYou would need to keep the money there for 4 years.

Compound interest

Compound interest is what banks use in real life. Compounding means you earn interest on the interest earned as well as on your principal. It is easiest to calculate and keep track of compound interest by using a table.

Compound interest

Suppose you have $1000 to save at a 5% rate and you keep it in the bank for 4 years. Simple interest would tell us to multiply 1000 (0.05) (4) and we would earn $200 for a total balance of $1200.

When we compound the interest, we must calculate one time period at a time.

Compound Interest

Beginning Balance Interest Balance

Year 1: $400 400(.05) = 20.00 $420

Year 2:

Year 3:

Year 4:

Compound Interest

Beginning Balance Interest Balance

Year 1: $400 400(.05) = 20.00 $420

Year 2: $420 420(.05) = 21.00 $441

Year 3:

Year 4:

Compound Interest

Beginning Balance Interest Balance

Year 1: $400 400(.05) = 20.00 $420

Year 2: $420 420(.05) = 21.00 $441

Year 3: $441 441(.05) = 22.05 $463.05

Year 4:

Compound Interest

Beginning Balance Interest Balance

Year 1: $400 400(.05) = 20.00 $420

Year 2: $420 420(.05) = 21.00 $441

Year 3: $441 441(.05) = 22.05 $463.05

Year 4: $463.05 463.05(.05) = 23.15 $486.20

Try This

Make a table to calculate the ending balance after saving $1000 at a 7% rate for 3 years.

Beginning Balance Interest Balance

Year 1:

Year 2:

Year 3:

Try This

Make a table to calculate the ending balance after saving $1000 at a 7% rate for 3 years.

Beginning Balance Interest Balance

Year 1: $1000 1000 (.07) = 70 $1070

Year 2:

Year 3:

Try This

Make a table to calculate the ending balance after saving $1000 at a 7% rate for 3 years.

Beginning Balance Interest Balance

Year 1: $1000 1000 (.07) = 70 $1070

Year 2: $1070 1070 (.07) = 74.90 $1144.90

Year 3:

Try This

Make a table to calculate the ending balance after saving $1000 at a 7% rate for 3 years.

Beginning Balance Interest Balance

Year 1: $1000 1000 (.07) = 70 $1070

Year 2: $1070 1070 (.07) = 74.90 $1144.49

Year 3: $1144.90 1144.90(.07)=80.14 $1225.04

Take it Further

In our previous example, we found that that balance after saving $1000 for 3 years at a 7% rate would be $1225.04

Compare this to simple interest:

I = prt I = 1000(0.07) (3) = $210

Added to the original 1000 we would have a balance of $1210

Cont.

You might be thinking big deal. . . It’s only $15.04 more with compounding.

True, but in real life, compounding occurs daily.

Also, when the numbers are large, the interest builds even more.

Cont.

In real life, the interest rates are about the same. . .around 4% or 5%.

But if you have a lot of money to invest or a lot of time to let it sit, compounding is powerful.

Believe it or not, if a rich uncle gave you $10,000 On the day you were born, and you invested it at a 5% rate and you left it there until you retire at age 65. . .

Cont.

You would have a balance of more than ¼ million dollars at retirement.

The total would be $269,750.

At a rate of 6% the total would be$521,350.

And if you got a rate of 8% the total would be$1,811,690!!!