$1000 is invested at 5% interest compounded yearly. How much is in… Step by Step

Step by step

The question

Question: $1000 is invested at 5% interest compounded yearly.

How much is in the account after 3 years?

1 Read the numbers

P is the money put in: $1000.

P = $1000: the money put in

r is the rate.

5% is 5/100: 0.05.

r = 5% = 0.05

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: 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 rate goes in as a decimal: 0.05, not 5.

Careful: not 1000 × 1.05³ ✗

2 Put them in

We put the numbers in.

A = 1000(1 + 0.051)^{1 × 3}

3 Work it out

Inside the bracket first.

The power: 1 times 3 is 3.

1 × 3 = 3

1 + 0.05 is 1.05.

So A is 1000 times 1.05 to the power 3.

A = 1000 × 1.05³

With a calculator, that power is about 1.15763.

1.05³ ≈ 1.15763

Now times 1000.

A ≈ 1000 × 1.15763

1157.625...

Money is rounded to cents: about $1157.63.

A ≈ $1157.63

4 Check

Let's check by going back: 1157.63 divided by 1.15763 is about $1000, the money put in.

$1157.63 ÷ 1.15763 ≈ $1000

And it makes sense.

Simple interest would give $1150.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $1000 + $150 = $1150 < $1157.63

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer