$800 is invested at 4% interest compounded yearly. How much is in… Step by Step

Step by step

The question

Question: $800 is invested at 4% interest compounded yearly.

How much is in the account after 2 years?

1 Read the numbers

P is the money put in: $800.

P = $800: the money put in

r is the rate.

4% is 4/100: 0.04.

r = 4% = 0.04

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: 2.

t = 2 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: 0.04, not 4.

Careful: not 800 × 1.04² ✗

2 Put them in

We put the numbers in.

A = 800(1 + 0.041)^{1 × 2}

3 Work it out

Inside the bracket first.

The power: 1 times 2 is 2.

1 × 2 = 2

1 + 0.04 is 1.04.

So A is 800 times 1.04 to the power 2.

A = 800 × 1.04²

With a calculator, that power is about 1.0816.

1.04² ≈ 1.0816

Now times 800.

A ≈ 800 × 1.0816

865.28...

Money is rounded to cents: about $865.28.

A ≈ $865.28

4 Check

Let's check by going back: 865.28 divided by 1.0816 is about $800, the money put in.

$865.28 ÷ 1.0816 ≈ $800

And it makes sense.

Simple interest would give $864.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $800 + $64 = $864 < $865.28

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer