Step by step
The question
Question: $3000 is invested at 2.5% interest compounded yearly.
How much is in the account after 4 years?
1 Read the numbers
P is the money put in: $3000.
r is the rate.
2.5% is 2.5/100: 0.025.
n is how many times a year the interest is added: once a year, so n = 1.
t is the time in years: 4.
2 Find the rule
Let's see one year first.
The interest is 2.5% of the money: 0.025 times 3000.
The money plus its interest is 3000 lots of 1, plus 3000 lots of 0.025: 3000 times 1 + 0.025, which is times 1.025.
Next year, the interest is on the new amount.
So again times 1.025.
4 years: times 1.025, 4 times.
That is 1.025 to the power 4.
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 + 0.025 is 1.025.
Not 1 + 2.5 = 3.5.
3 Put them in
We put the numbers in.
4 Work it out
Inside the bracket first: 0.025 divided by 1 is 0.025.
The power: 1 times 4 is 4.
1 + 0.025 is 1.025.
So A is 3000 times 1.025 to the power 4.
With a calculator, that power is about 1.10381289.
Now times 3000.
That is 3311.4387.
Money is rounded to cents: about $3311.44.
5 Check
Let's check by going back.
Dividing undoes the times: 3311.44 divided by 1.10381289 is about $3000, the money put in.
And it makes sense.
Simple interest is only on the money put in: 3000 times 0.025 times 4 is $300.
That gives $3300.00.
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.