$4000 is invested at 3% interest compounded continuously. How much… Step by Step

Step by step

The question

Question: $4000 is invested at 3% interest compounded continuously.

How much is in the account after 6 years?

1 Read the numbers

P is the money put in: $4000.

P = $4000: the money put in

r is the rate.

3% is 3/100: 0.03.

r = 3% = 0.03

t is the time in years: 6.

t = 6 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: 0.03, not 3.

Careful: not r = 3 ✗

2 Put them in

We put the numbers in.

A = 4000 × e^{0.03 × 6}

3 Work it out

The power first: 0.03 times 6 is 0.18.

0.03 × 6 = 0.18

So A is 4000 times e to the power 0.18.

A = 4000 × e^0.18

With a calculator, e to the power 0.18 is about 1.19722.

e^0.18 ≈ 1.19722

Now times 4000.

A ≈ 4000 × 1.19722

4788.8695...

Money is rounded to cents: about $4788.87.

A ≈ $4788.87

4 Check

Let's check by going back: 4788.87 divided by 1.19722 is about $4000, the money put in.

$4788.87 ÷ 1.19722 ≈ $4000

And it makes sense.

Simple interest would give $4720.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $4000 + $720 = $4720 < $4788.87

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer