simple and compound interest - edl · simple and compound interest interest is a term used in...
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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. . .