$1,500 is deposited at the end of each year into an account paying… Step by Step

Step by step

The question

Question: $1500 is deposited at the end of each year into an account paying 6% compounded yearly.

How much is in the account after 25 years?

1 Read the numbers

PMT is the money put in each time: $1500.

r is the yearly rate: 6% is 0.06.

PMT = $1,500 each time, r = 6% = 0.06

n is how many times a year: once.

t is the time: 25 years.

n = 1 a year, t = 25 years

2 Per payment

Interest is added each year.

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

0.06 divided by 1 is 0.06.

i = rn = 0.061 = 0.06

i = the rate each year

And N is how many deposits: 1 times 25 is 25.

N = n × t = 1 × 25 = 25

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 0.06 is 1.06.

FV = 1500 × 1.06²⁵ − 10.06

4 Work it out

With a calculator, 1.06 to the power 25 is about 4.29187.

Minus 1, divided by 0.06: about 54.8645.

1.06²⁵ ≈ 4.29187

(4.29187 − 1) ÷ 0.06 ≈ 54.8645

So FV is 1500 times 54.8645.

FV ≈ 1500 × 54.8645

Money is rounded to cents: about 82296 dollars and 77 cents.

FV ≈ $82,296.77

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $1,500 × 25 ✗

5 Check

Let's check.

The deposits alone are 1500 times 25: $37500.

The account has more, because of the interest.

deposits: $1,500 × 25 = $37,500 < $82,296.77

The interest earned is 44796 dollars and 77 cents.

So it makes sense!

interest: $82,296.77 − $37,500 = $44,796.77

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer