$2,000 is deposited at the end of each year into an account paying… Step by Step

Step by step

The question

Question: $2000 is deposited at the end of each year into an account paying 4% compounded annually.

How much is in the account after 6 years?

1 Read the numbers

PMT is the money put in each time: $2000.

r is the yearly rate: 4% is 0.04.

PMT = $2,000 each time, r = 4% = 0.04

n is how many times a year: once.

t is the time: 6 years.

n = 1 a year, t = 6 years

2 Per payment

Interest is added each year.

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

0.04 divided by 1 is 0.04.

i = rn = 0.041 = 0.04

i = the rate each year

And N is how many deposits: 1 times 6 is 6.

N = n × t = 1 × 6 = 6

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 0.04 is 1.04.

FV = 2000 × 1.04⁶ − 10.04

4 Work it out

With a calculator, 1.04 to the power 6 is about 1.26532.

Minus 1, divided by 0.04: about 6.63298.

1.04⁶ ≈ 1.26532

(1.26532 − 1) ÷ 0.04 ≈ 6.63298

So FV is 2000 times 6.63298.

FV ≈ 2000 × 6.63298

Money is rounded to cents: about 13265 dollars and 95 cents.

FV ≈ $13,265.95

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $2,000 × 6 ✗

5 Check

Let's check.

The deposits alone are 2000 times 6: $12000.

The account has more, because of the interest.

deposits: $2,000 × 6 = $12,000 < $13,265.95

The interest earned is 1265 dollars and 95 cents.

So it makes sense!

interest: $13,265.95 − $12,000 = $1,265.95

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer