Step by step
The question
Question: $4500 is invested at 3.2% interest compounded yearly.
How much is in the account after 5 years?
1 Read the numbers
P is the money put in: $4500.
r is the rate.
3.2% is 3.2/100: 0.032.
n is how many times a year the interest is added: once a year, so n = 1.
t is the time in years: 5.
2 Find the rule
Let's see one year first.
The interest is 3.2% of the money: 0.032 times 4500.
The money plus its interest is 4500 lots of 1, plus 4500 lots of 0.032: 4500 times 1 + 0.032, which is times 1.032.
Next year, the interest is on the new amount.
So again times 1.032.
5 years: times 1.032, 5 times.
That is 1.032 to the power 5.
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 + 0.032 is 1.032.
Not 1 + 3.2 = 4.2.
3 Put them in
We put the numbers in.
4 Work it out
Inside the bracket first: 0.032 divided by 1 is 0.032.
The power: 1 times 5 is 5.
1 + 0.032 is 1.032.
So A is 4500 times 1.032 to the power 5.
With a calculator, that power is about 1.17057296.
Now times 4500.
That is 5267.5783.
Money is rounded to cents: about $5267.58.
5 Check
Let's check by going back.
Dividing undoes the times: 5267.58 divided by 1.17057296 is about $4500, the money put in.
And it makes sense.
Simple interest is only on the money put in: 4500 times 0.032 times 5 is $720.
That gives $5220.
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.