$50 is deposited at the end of each month into an account paying 6%… Step by Step

Step by step

The question

Question: $50 is deposited at the end of each month into an account paying 6% compounded monthly.

How much is in the account after 4 years?

1 Read the numbers

PMT is the money put in each time: $50.

r is the yearly rate: 6% is 0.06.

PMT = $50 each time, r = 6% = 0.06

n is how many times a year: 12.

t is the time: 4 years.

n = 12 a year, t = 4 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 4 is 48.

N = n × t = 12 × 4 = 48

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 = 50 × 1.005⁴⁸ − 10.005

4 Work it out

With a calculator, 1.005 to the power 48 is about 1.27049.

Minus 1, divided by 0.005: about 54.0978.

1.005⁴⁸ ≈ 1.27049

(1.27049 − 1) ÷ 0.005 ≈ 54.0978

So FV is 50 times 54.0978.

FV ≈ 50 × 54.0978

Money is rounded to cents: about 2704 dollars and 89 cents.

FV ≈ $2,704.89

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $50 × 48 ✗

5 Check

Let's check.

The deposits alone are 50 times 48: $2400.

The account has more, because of the interest.

deposits: $50 × 48 = $2,400 < $2,704.89

The interest earned is 304 dollars and 89 cents.

So it makes sense!

interest: $2,704.89 − $2,400 = $304.89

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer