Step by step
The question
Question: $2000 is invested at 6% interest compounded twice a year.
How much is in the account after 2 years?
1 Read the numbers
P is the money put in: $2000.
r is the rate.
6% is 6/100: 0.06.
n is how many times a year the interest is added: twice a year, so n = 2.
t is the time in years: 2.
The amount after t years is A = P times (1 + r/n) to the power nt.
Each time, the money is multiplied by 1 + r over n.
Careful!
The 6% is for a whole year.
Each time we add only r/n: 0.06 divided by 2.
2 Put them in
We put the numbers in.
3 Work it out
Inside the bracket first: 0.06 divided by 2 is 0.03.
The power: 2 times 2 is 4.
1 + 0.03 is 1.03.
So A is 2000 times 1.03 to the power 4.
With a calculator, that power is about 1.12551.
Now times 2000.
2251.0176...
Money is rounded to cents: about $2251.02.
4 Check
Let's check by going back: 2251.02 divided by 1.12551 is about $2000, the money put in.
And it makes sense.
Simple interest would give $2240.
Interest on interest gives a bit more.
So the answer is right!
Let's look back.
First: read the numbers.
Then: put them in.
Then: work it out.
Last: check.