$400 is deposited at the end of each month into an account paying… Step by Step

Step by step

The question

Question: $400 is deposited at the end of each month into an account paying 1.2% compounded monthly.

How much is in the account after 1 year?

1 Read the numbers

PMT is the money put in each time: $400.

r is the yearly rate: 1.2% is 0.012.

PMT = $400 each time, r = 1.2% = 0.012

n is how many times a year: 12.

t is the time: 1 years.

n = 12 a year, t = 1 years

2 Per payment

Interest is added each month.

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

0.012 divided by 12 is 0.001.

i = rn = 0.01212 = 0.001

i = the rate each month

And N is how many deposits: 12 times 1 is 12.

N = n × t = 12 × 1 = 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 0.001 is 1.001.

FV = 400 × 1.001¹² − 10.001

4 Work it out

With a calculator, 1.001 to the power 12 is about 1.01207.

Minus 1, divided by 0.001: about 12.0662.

1.001¹² ≈ 1.01207

(1.01207 − 1) ÷ 0.001 ≈ 12.0662

So FV is 400 times 12.0662.

FV ≈ 400 × 12.0662

Money is rounded to cents: about 4826 dollars and 49 cents.

FV ≈ $4,826.49

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $400 × 12 ✗

5 Check

Let's check.

The deposits alone are 400 times 12: $4800.

The account has more, because of the interest.

deposits: $400 × 12 = $4,800 < $4,826.49

The interest earned is 26 dollars and 49 cents.

So it makes sense!

interest: $4,826.49 − $4,800 = $26.49

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer