$200 is deposited at the end of each month into an account paying 6%… Step by Step

Step by step

The question

Question: $200 is deposited at the end of each month into an account paying 6% compounded monthly.

How much is in the account after 5 years?

1 Read the numbers

PMT is the money put in each time: $200.

r is the yearly rate: 6% is 0.06.

PMT = $200 each time, r = 6% = 0.06

n is how many times a year: 12.

t is the time: 5 years.

n = 12 a year, t = 5 years

2 Per payment

Interest is added each month.

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

0.06 divided by 12 is 0.005.

i = rn = 0.0612 = 0.005

i = the rate each month

And N is how many deposits: 12 times 5 is 60.

N = n × t = 12 × 5 = 60

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 = 200 × 1.005⁶⁰ − 10.005

4 Work it out

With a calculator, 1.005 to the power 60 is about 1.34885.

Minus 1, divided by 0.005: about 69.77.

1.005⁶⁰ ≈ 1.34885

(1.34885 − 1) ÷ 0.005 ≈ 69.77

So FV is 200 times 69.77.

FV ≈ 200 × 69.77

Money is rounded to cents: about 13954 dollars and 1 cent.

FV ≈ $13,954.01

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $200 × 60 ✗

5 Check

Let's check.

The deposits alone are 200 times 60: $12000.

The account has more, because of the interest.

deposits: $200 × 60 = $12,000 < $13,954.01

The interest earned is 1954 dollars and 1 cent.

So it makes sense!

interest: $13,954.01 − $12,000 = $1,954.01

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer