Hi Nina,
If you have $1250 invested for 1 year at 6% per year then at the end of the year you have $1250 plus 6% of $1250. Thus at the end of the first year you have
$1250 + ^{6}/_{100} $1250
= $1250 + 0.06
$1250
= 1.06 $1250
= $1325
Now, in the second year you have $1325 invested at 6% for 1 year so how much do you have at the end of the second year?
In the third year you have that much invested at 6% for 1 year so how much do you have at the end of the third year?
That's the amount that will be in your account at the end of the third year but can you see how to get this number in one calculation rather than three?
Penny
Hi Nina.
First, recall that a percentage is just the amount out of 100. Compount interest is interest that is paid and then is added to the total so that future interest is paid on the sum.
Here's an example: Start with $1000 at 10% compound annual interest. Year 0: You have $1000 total.
Year 1. You have earned interest of 10% x $1000. That is $100. This gets added to the $1000 you had. So now your total is $1000 + $100 = $1100.
Year 2: You have earned interest of 10% x $1100. That is $110. This gets added to the $1100 you had. So now your total is $1100 + $110 = $1210.
Year 3: 10% of $1210 is $121. $121 + $1210 = $1331.
and so on.
When you multiply something by 1, you get the original number. So here is a shortcut:
new total = previous total x (1 + interest rate)
For example for year 1 above:
new total = $1000 x (1 + 10%) = $1000 x (1 + 0.10) = $1000 x 1.10 = $1100.
In fact, you could keep doing this repeatedly:
total for year 3 would have three multiplications:
total for year 3 = $1000 x (1 + 10% ) x (1 + 10%) x (1 + 10%)
= $1000 x 1.10 x 1.10 x 1.10
= $1331.
That's a good shortcut you can use with your question.
Stephen La Rocque>
