$1200 is invested at 6% interest compounded quarterly. How much is… Step by Step

Step by step

The question

Question: $1200 is invested at 6% interest compounded quarterly.

How much is in the account after 5 years?

1 Read the numbers

P is the money put in: $1200.

P = $1200: the money put in

r is the rate.

6% is 6/100: 0.06.

r = 6% = 0.06

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: 5.

t = 5 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 6% is for a whole year.

Each time we add only r/n: 0.06 divided by 4.

Careful: not 1200 × 1.06²⁰ ✗

2 Put them in

We put the numbers in.

A = 1200(1 + 0.064)^{4 × 5}

3 Work it out

Inside the bracket first: 0.06 divided by 4 is 0.015.

The power: 4 times 5 is 20.

0.06 ÷ 4 = 0.015

4 × 5 = 20

1 + 0.015 is 1.015.

So A is 1200 times 1.015 to the power 20.

A = 1200 × 1.015²⁰

With a calculator, that power is about 1.34686.

1.015²⁰ ≈ 1.34686

Now times 1200.

A ≈ 1200 × 1.34686

1616.226...

Money is rounded to cents: about $1616.23.

A ≈ $1616.23

4 Check

Let's check by going back: 1616.23 divided by 1.34686 is about $1200, the money put in.

$1616.23 ÷ 1.34686 ≈ $1200

And it makes sense.

Simple interest would give $1560.

Interest on interest gives a bit more.

So the answer is right!

simple interest: $1200 + $360 = $1560 < $1616.23

Let's look back.

First: read the numbers.

Then: put them in.

Then: work it out.

Last: check.

Answer