$6000 is invested at 2.5% interest compounded quarterly. How much is… Step by Step

Step by step

The question

Question: $6000 is invested at 2.5% interest compounded quarterly.

How much is in the account after 8 years?

1 Read the numbers

P is the money put in: $6000.

P = $6000: the money put in

r is the rate.

2.5% is 2.5/100: 0.025.

r = 2.5% = 0.025

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: 8.

t = 8 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 2.5% is for a whole year.

Each time we add only r/n: 0.025 divided by 4.

Careful: not 6000 × 1.025³² ✗

2 Put them in

We put the numbers in.

A = 6000(1 + 0.0254)^{4 × 8}

3 Work it out

Inside the bracket first: 0.025 divided by 4 is 0.00625.

The power: 4 times 8 is 32.

0.025 ÷ 4 = 0.00625

4 × 8 = 32

1 + 0.00625 is 1.00625.

So A is 6000 times 1.00625 to the power 32.

A = 6000 × 1.00625³²

With a calculator, that power is about 1.22064.

1.00625³² ≈ 1.22064

Now times 6000.

A ≈ 6000 × 1.22064

7323.8567...

Money is rounded to cents: about $7323.86.

A ≈ $7323.86

4 Check

Let's check by going back: 7323.86 divided by 1.22064 is about $6000, the money put in.

$7323.86 ÷ 1.22064 ≈ $6000

And it makes sense.

Simple interest would give $7200.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $6000 + $1200 = $7200 < $7323.86

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer