$10000 is invested at 5% interest compounded continuously. How much… Step by Step

Step by step

The question

Question: $10000 is invested at 5% interest compounded continuously.

How much is in the account after 18 years?

1 Read the numbers

P is the money put in: $10000.

P = $10000: the money put in

r is the rate.

5% is 5/100: 0.05.

r = 5% = 0.05

t is the time in years: 18.

t = 18 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: 0.05, not 5.

Careful: not r = 5 ✗

2 Put them in

We put the numbers in.

A = 10000 × e^{0.05 × 18}

3 Work it out

The power first: 0.05 times 18 is 0.9.

0.05 × 18 = 0.9

So A is 10000 times e to the power 0.9.

A = 10000 × e^0.9

With a calculator, e to the power 0.9 is about 2.4596.

e^0.9 ≈ 2.4596

Now times 10000.

A ≈ 10000 × 2.4596

24596.0311...

Money is rounded to cents: about $24596.03.

A ≈ $24596.03

4 Check

Let's check by going back: 24596.03 divided by 2.4596 is about $10000, the money put in.

$24596.03 ÷ 2.4596 ≈ $10000

And it makes sense.

Simple interest would give $19000.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $10000 + $9000 = $19000 < $24596.03

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer