$600 is invested at 6% interest compounded monthly. How much is in… Step by Step

Step by step

The question

Question: $600 is invested at 6% interest compounded monthly.

How much is in the account after 3 years?

1 Read the numbers

P is the money put in: $600.

P = $600: the money put in

r is the rate.

6% is 6/100: 0.06.

r = 6% = 0.06

n is how many times a year the interest is added: monthly, so n = 12.

n = 12: monthly: 12 times a year

t is the time in years: 3.

t = 3 years

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.

A = P(1 + rn)^nt

Careful!

The 6% is for a whole year.

Each time we add only r/n: 0.06 divided by 12.

Careful: not 600 × 1.06³⁶ ✗

2 Put them in

We put the numbers in.

A = 600(1 + 0.0612)^{12 × 3}

3 Work it out

Inside the bracket first: 0.06 divided by 12 is 0.005.

The power: 12 times 3 is 36.

0.06 ÷ 12 = 0.005

12 × 3 = 36

1 + 0.005 is 1.005.

So A is 600 times 1.005 to the power 36.

A = 600 × 1.005³⁶

With a calculator, that power is about 1.19668.

1.005³⁶ ≈ 1.19668

Now times 600.

A ≈ 600 × 1.19668

718.0083...

Money is rounded to cents: about $718.01.

A ≈ $718.01

4 Check

Let's check by going back: 718.01 divided by 1.19668 is about $600, the money put in.

$718.01 ÷ 1.19668 ≈ $600

And it makes sense.

Simple interest would give $708.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $600 + $108 = $708 < $718.01

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer