$500 is deposited at the end of each quarter into an account paying… Step by Step

Step by step

The question

Question: $500 is deposited at the end of each quarter into an account paying 4% compounded quarterly.

How much is in the account after 3 years?

1 Read the numbers

PMT is the money put in each time: $500.

r is the yearly rate: 4% is 0.04.

PMT = $500 each time, r = 4% = 0.04

n is how many times a year: 4.

t is the time: 3 years.

n = 4 a year, t = 3 years

2 Per payment

Interest is added each quarter.

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

0.04 divided by 4 is 0.01.

i = rn = 0.044 = 0.01

i = the rate each quarter

And N is how many deposits: 4 times 3 is 12.

N = n × t = 4 × 3 = 12

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 0.01 is 1.01.

FV = 500 × 1.01¹² − 10.01

4 Work it out

With a calculator, 1.01 to the power 12 is about 1.12683.

Minus 1, divided by 0.01: about 12.6825.

1.01¹² ≈ 1.12683

(1.12683 − 1) ÷ 0.01 ≈ 12.6825

So FV is 500 times 12.6825.

FV ≈ 500 × 12.6825

Money is rounded to cents: about 6341 dollars and 25 cents.

FV ≈ $6,341.25

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $500 × 12 ✗

5 Check

Let's check.

The deposits alone are 500 times 12: $6000.

The account has more, because of the interest.

deposits: $500 × 12 = $6,000 < $6,341.25

The interest earned is 341 dollars and 25 cents.

So it makes sense!

interest: $6,341.25 − $6,000 = $341.25

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer