Step by step
The question
Question: $5000 is invested at 3.5% interest compounded yearly.
How much is in the account after 6 years?
1 Read the numbers
P is the money put in: $5000.
r is the rate.
3.5% is 3.5/100: 0.035.
n is how many times a year the interest is added: once a year, so n = 1.
t is the time in years: 6.
2 Find the rule
Let's see one year first.
The interest is 3.5% of the money: 0.035 times 5000.
The money plus its interest is 5000 lots of 1, plus 5000 lots of 0.035: 5000 times 1 + 0.035, which is times 1.035.
Next year, the interest is on the new amount.
So again times 1.035.
6 years: times 1.035, 6 times.
That is 1.035 to the power 6.
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 + 0.035 is 1.035.
Not 1 + 3.5 = 4.5.
3 Put them in
We put the numbers in.
4 Work it out
Inside the bracket first: 0.035 divided by 1 is 0.035.
The power: 1 times 6 is 6.
1 + 0.035 is 1.035.
So A is 5000 times 1.035 to the power 6.
With a calculator, that power is about 1.22925533.
Now times 5000.
That is 6146.2766.
Money is rounded to cents: about $6146.28.
5 Check
Let's check by going back.
Dividing undoes the times: 6146.28 divided by 1.22925533 is about $5000, the money put in.
And it makes sense.
Simple interest is only on the money put in: 5000 times 0.035 times 6 is $1050.00.
That gives $6050.
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.