Step by step
The question
Question: A = 1000 × (1.05)ᵗ is the money in a bank account, in dollars, t years from now.
What does 1.05 mean?
We write the equation big, so we can label it.
1 What the letters mean
A is the money, in dollars.
t is the number of years.
It is the small raised number, the power: how many times we multiply by 1.05.
2 Make a small table
To see what each number does, we try a few years: 0, 1 and 2.
0 is where it starts.
t = 0: no years have passed, so we multiply by 1.05 zero times.
That is why 1.05 to the power 0 is 1.
1000 times 1 is 1000.
t = 1: 1.05 to the power 1 is just 1.05.
1000 times 1.05 is 1050.
t = 2: 1.05 squared is 1.05 times 1.05.
1000 times 1.05 is 1050.
Times 1.05 again: 1050 times 1.05 is 1102.5.
Look at the values of A: 1000, 1050, 1102.5.
Each time t goes up 1, A is multiplied by 1.05.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
1000 is A at t = 0: the first number in the table.
So 1000 is the money at the start.
1.05 is what we multiply by, once for each year.
That is the power t: it counts the years.
4 Write it as a percent
A percent is out of 100: one whole is 100%.
So we multiply by 100.
1.05 times 100 is 105.
So 1.05 is 105%.
105% is all of it, 100%, plus 5% more.
Careful!
105% is the new amount: the 100% it had, plus 5%.
The growth is only the part above 100%: 5%.
5 Say it in words
So 1.05 means: the money goes up by 5% each year.
6 Check
Let's check the 5%.
5% is 5/100, that is 0.05.
5% of 1000 is 0.05 times 1000: 50.
1000 plus 50 is 1050: the same as the table at t = 1.
It works!
Let's look back.
First: what the letters mean.
Then: make a small table.
Then: find the numbers in the table.
Then: write it as a percent.
Then: say it in words.
Last: check.