$150 is deposited at the end of each month into an account paying… Step by Step

Step by step

The question

Question: $150 is deposited at the end of each month into an account paying 2.4% compounded monthly.

How much is in the account after 3 years?

1 Read the numbers

PMT is the money put in each time: $150.

r is the yearly rate: 2.4% is 0.024.

PMT = $150 each time, r = 2.4% = 0.024

n is how many times a year: 12.

t is the time: 3 years.

n = 12 a year, t = 3 years

2 Per payment

Interest is added each month.

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

0.024 divided by 12 is 0.002.

i = rn = 0.02412 = 0.002

i = the rate each month

And N is how many deposits: 12 times 3 is 36.

N = n × t = 12 × 3 = 36

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 0.002 is 1.002.

FV = 150 × 1.002³⁶ − 10.002

4 Work it out

With a calculator, 1.002 to the power 36 is about 1.07458.

Minus 1, divided by 0.002: about 37.289.

1.002³⁶ ≈ 1.07458

(1.07458 − 1) ÷ 0.002 ≈ 37.289

So FV is 150 times 37.289.

FV ≈ 150 × 37.289

Money is rounded to cents: about 5593 dollars and 36 cents.

FV ≈ $5,593.36

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $150 × 36 ✗

5 Check

Let's check.

The deposits alone are 150 times 36: $5400.

The account has more, because of the interest.

deposits: $150 × 36 = $5,400 < $5,593.36

The interest earned is 193 dollars and 36 cents.

So it makes sense!

interest: $5,593.36 − $5,400 = $193.36

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer