$900 is invested at 9% interest compounded continuously. How much is… Step by Step

Step by step

The question

Question: $900 is invested at 9% interest compounded continuously.

How much is in the account after 3 years?

1 Read the numbers

P is the money put in: $900.

P = $900: the money put in

r is the rate.

9% is 9/100: 0.09.

r = 9% = 0.09

t is the time in years: 3.

t = 3 years

With continuous interest, the amount is A = P times e to the power rt.

e is the special number from the ln lesson, about 2.718.

A = Pe^rt

e ≈ 2.718

Careful!

The rate goes in as a decimal: 0.09, not 9.

Careful: not r = 9 ✗

2 Put them in

We put the numbers in.

A = 900 × e^{0.09 × 3}

3 Work it out

The power first: 0.09 times 3 is 0.27.

0.09 × 3 = 0.27

So A is 900 times e to the power 0.27.

A = 900 × e^0.27

With a calculator, e to the power 0.27 is about 1.30996.

e^0.27 ≈ 1.30996

Now times 900.

A ≈ 900 × 1.30996

1178.968...

Money is rounded to cents: about $1178.97.

A ≈ $1178.97

4 Check

Let's check by going back: 1178.97 divided by 1.30996 is about $900, the money put in.

$1178.97 ÷ 1.30996 ≈ $900

And it makes sense.

Simple interest would give $1143.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $900 + $243 = $1143 < $1178.97

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer