Step by step
The question
Question: $2000 is invested at 4% interest compounded yearly.
How much is in the account after 3 years?
1 Read the numbers
P is the money put in: $2000.
r is the rate.
4% is 4/100: 0.04.
n is how many times a year the interest is added: once a year, so n = 1.
t is the time in years: 3.
2 Find the rule
Let's see one year first.
The interest is 4% of the money: 0.04 times 2000.
The money plus its interest is 2000 lots of 1, plus 2000 lots of 0.04: 2000 times 1 + 0.04, which is times 1.04.
Next year, the interest is on the new amount.
So again times 1.04.
3 years: times 1.04, 3 times.
That is 1.04 to the power 3.
So the amount after t years is A = P times (1 + r/n) to the power nt.
n times t counts how many times the interest is added.
Here n = 1: once a year, so r/n is just r.
Careful!
The rate goes in as a decimal: 1 + 0.04 is 1.04.
Not 1 + 4 = 5.
3 Put them in
We put the numbers in.
4 Work it out
Inside the bracket first: 0.04 divided by 1 is 0.04.
The power: 1 times 3 is 3.
1 + 0.04 is 1.04.
So A is 2000 times 1.04 to the power 3.
With a calculator, that power is about 1.124864.
Now times 2000.
That is 2249.728.
Money is rounded to cents: about $2249.73.
5 Check
Let's check by going back.
Dividing undoes the times: 2249.73 divided by 1.124864 is about $2000, the money put in.
And it makes sense.
Simple interest is only on the money put in: 2000 times 0.04 times 3 is $240.
That gives $2240.
Interest on interest gives a bit more.
So the answer makes sense!
Let's look back.
First: read the numbers.
Then: find the rule.
Then: put them in.
Then: work it out.
Last: check.