$600 is deposited at the end of each quarter into an account paying… Step by Step

Step by step

The question

Question: $600 is deposited at the end of each quarter into an account paying 2% compounded quarterly.

How much is in the account after 5 years?

1 Read the numbers

PMT is the money put in each time: $600.

r is the yearly rate: 2% is 0.02.

PMT = $600 each time, r = 2% = 0.02

n is how many times a year: 4.

t is the time: 5 years.

n = 4 a year, t = 5 years

2 Per payment

Interest is added each quarter.

The rate for one quarter is i: r over n.

0.02 divided by 4 is 0.005.

i = rn = 0.024 = 0.005

i = the rate each quarter

And N is how many deposits: 4 times 5 is 20.

N = n × t = 4 × 5 = 20

3 Use the formula

The future value FV is what the account holds at the end: PMT times, (1 + i) to the power N, minus 1, over i.

FV = PMT × (1 + i)^N − 1i

FV = future value: the money at the end

We put the numbers in: 1 plus 0.005 is 1.005.

FV = 600 × 1.005²⁰ − 10.005

4 Work it out

With a calculator, 1.005 to the power 20 is about 1.1049.

Minus 1, divided by 0.005: about 20.9791.

1.005²⁰ ≈ 1.1049

(1.1049 − 1) ÷ 0.005 ≈ 20.9791

So FV is 600 times 20.9791.

FV ≈ 600 × 20.9791

Money is rounded to cents: about 12587 dollars and 47 cents.

FV ≈ $12,587.47

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $600 × 20 ✗

5 Check

Let's check.

The deposits alone are 600 times 20: $12000.

The account has more, because of the interest.

deposits: $600 × 20 = $12,000 < $12,587.47

The interest earned is 587 dollars and 47 cents.

So it makes sense!

interest: $12,587.47 − $12,000 = $587.47

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer