$1000 is invested at 4% interest compounded quarterly. How much is… Step by Step

Step by step

The question

Question: $1000 is invested at 4% interest compounded quarterly.

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.

4% is 4/100: 0.04.

r = 4% = 0.04

n is how many times a year the interest is added: quarterly, so n = 4.

n = 4: quarterly: 4 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 4% is for a whole year.

Each time we add only r/n: 0.04 divided by 4.

Careful: not 1000 × 1.04¹² ✗

2 Put them in

We put the numbers in.

A = 1000(1 + 0.044)^{4 × 3}

3 Work it out

Inside the bracket first: 0.04 divided by 4 is 0.01.

The power: 4 times 3 is 12.

0.04 ÷ 4 = 0.01

4 × 3 = 12

1 + 0.01 is 1.01.

So A is 1000 times 1.01 to the power 12.

A = 1000 × 1.01¹²

With a calculator, that power is about 1.12683.

1.01¹² ≈ 1.12683

Now times 1000.

A ≈ 1000 × 1.12683

1126.825...

Money is rounded to cents: about $1126.83.

A ≈ $1126.83

4 Check

Let's check by going back: 1126.83 divided by 1.12683 is about $1000, the money put in.

$1126.83 ÷ 1.12683 ≈ $1000

And it makes sense.

Simple interest would give $1120.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $1000 + $120 = $1120 < $1126.83

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer