$3000 is invested at 2% interest compounded yearly. How much is in… Step by Step

Step by step

The question

Question: $3000 is invested at 2% interest compounded yearly.

How much is in the account after 5 years?

1 Read the numbers

P is the money put in: $3000.

P = $3000: the money put in

r is the rate.

2% is 2/100: 0.02.

r = 2% = 0.02

n is how many times a year the interest is added: once a year, so n = 1.

n = 1: once 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 rate goes in as a decimal: 0.02, not 2.

Careful: not 3000 × 1.02⁵ ✗

2 Put them in

We put the numbers in.

A = 3000(1 + 0.021)^{1 × 5}

3 Work it out

Inside the bracket first.

The power: 1 times 5 is 5.

1 × 5 = 5

1 + 0.02 is 1.02.

So A is 3000 times 1.02 to the power 5.

A = 3000 × 1.02⁵

With a calculator, that power is about 1.10408.

1.02⁵ ≈ 1.10408

Now times 3000.

A ≈ 3000 × 1.10408

3312.2424...

Money is rounded to cents: about $3312.24.

A ≈ $3312.24

4 Check

Let's check by going back: 3312.24 divided by 1.10408 is about $3000, the money put in.

$3312.24 ÷ 1.10408 ≈ $3000

And it makes sense.

Simple interest would give $3300.00.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $3000 + $300 = $3300.00 < $3312.24

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer