$1000 is invested at 6% interest compounded monthly. How much is in… Step by Step

Step by step

The question

Question: $1000 is invested at 6% interest compounded monthly.

How much is in the account after 5 years?

1 Read the numbers

P is the money put in: $1000.

P = $1000: 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: 5.

t = 5 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 1000 × 1.06⁶⁰ ✗

2 Put them in

We put the numbers in.

A = 1000(1 + 0.0612)^{12 × 5}

3 Work it out

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

The power: 12 times 5 is 60.

0.06 ÷ 12 = 0.005

12 × 5 = 60

1 + 0.005 is 1.005.

So A is 1000 times 1.005 to the power 60.

A = 1000 × 1.005⁶⁰

With a calculator, that power is about 1.34885.

1.005⁶⁰ ≈ 1.34885

Now times 1000.

A ≈ 1000 × 1.34885

1348.8502...

Money is rounded to cents: about $1348.85.

A ≈ $1348.85

4 Check

Let's check by going back: 1348.85 divided by 1.34885 is about $1000, the money put in.

$1348.85 ÷ 1.34885 ≈ $1000

And it makes sense.

Simple interest would give $1300.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $1000 + $300 = $1300 < $1348.85

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer