$250 is deposited at the end of each month into an account paying… Step by Step

Step by step

The question

Question: $250 is deposited at the end of each month into an account paying 3.75% compounded monthly.

How much is in the account after 8 years?

1 Read the numbers

PMT is the money put in each time: $250.

r is the yearly rate: 3.75% is 0.0375.

PMT = $250 each time, r = 3.75% = 0.0375

n is how many times a year: 12.

t is the time: 8 years.

n = 12 a year, t = 8 years

2 Per payment

Interest is added each month.

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

0.0375 divided by 12 is 0.003125.

i = rn = 0.037512 = 0.003125

i = the rate each month

And N is how many deposits: 12 times 8 is 96.

N = n × t = 12 × 8 = 96

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 0.003125 is 1.003125.

FV = 250 × 1.003125⁹⁶ − 10.003125

4 Work it out

With a calculator, 1.003125 to the power 96 is about 1.34923.

Minus 1, divided by 0.003125: about 111.753.

1.003125⁹⁶ ≈ 1.34923

(1.34923 − 1) ÷ 0.003125 ≈ 111.753

So FV is 250 times 111.753.

FV ≈ 250 × 111.753

Money is rounded to cents: about 27938 dollars and 20 cents.

FV ≈ $27,938.20

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $250 × 96 ✗

5 Check

Let's check.

The deposits alone are 250 times 96: $24000.

The account has more, because of the interest.

deposits: $250 × 96 = $24,000 < $27,938.20

The interest earned is 3938 dollars and 20 cents.

So it makes sense!

interest: $27,938.20 − $24,000 = $3,938.20

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer