Step by step
The question
Question: $750 is invested at 7% interest compounded daily.
How much is in the account after 4 years?
1 Read the numbers
P is the money put in: $750.
r is the rate.
7% is 7/100: 0.07.
n is how many times a year the interest is added: daily, so n = 365.
t is the time in years: 4.
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 7% is for a whole year.
Each time we add only r/n: 0.07 divided by 365.
2 Put them in
We put the numbers in.
3 Work it out
Inside the bracket first: 0.07 divided by 365 is about 0.000191781.
The power: 365 times 4 is 1460.
So A is 750 times the bracket to the power 1460.
With a calculator, that power is about 1.32309.
Now times 750.
992.3207...
Money is rounded to cents: about $992.32.
4 Check
Let's check by going back: 992.32 divided by 1.32309 is about $750, the money put in.
And it makes sense.
Simple interest would give $960.
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.