$2000 is invested at 3% interest compounded quarterly. How much is… Step by Step

Step by step

The question

Question: $2000 is invested at 3% interest compounded quarterly.

How much is in the account after 4 years?

1 Read the numbers

P is the money put in: $2000.

P = $2000: the money put in

r is the rate.

3% is 3/100: 0.03.

r = 3% = 0.03

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: 4.

t = 4 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 3% is for a whole year.

Each time we add only r/n: 0.03 divided by 4.

Careful: not 2000 × 1.03¹⁶ ✗

2 Put them in

We put the numbers in.

A = 2000(1 + 0.034)^{4 × 4}

3 Work it out

Inside the bracket first: 0.03 divided by 4 is 0.0075.

The power: 4 times 4 is 16.

0.03 ÷ 4 = 0.0075

4 × 4 = 16

1 + 0.0075 is 1.0075.

So A is 2000 times 1.0075 to the power 16.

A = 2000 × 1.0075¹⁶

With a calculator, that power is about 1.12699.

1.0075¹⁶ ≈ 1.12699

Now times 2000.

A ≈ 2000 × 1.12699

2253.9842...

Money is rounded to cents: about $2253.98.

A ≈ $2253.98

4 Check

Let's check by going back: 2253.98 divided by 1.12699 is about $2000, the money put in.

$2253.98 ÷ 1.12699 ≈ $2000

And it makes sense.

Simple interest would give $2240.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $2000 + $240 = $2240 < $2253.98

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer