$1,000 is deposited at the end of each year into an account paying… Step by Step

Step by step

The question

Question: $1000 is deposited at the end of each year into an account paying 5% compounded yearly.

How much is in the account after 10 years?

1 Read the numbers

PMT is the money put in each time: $1000.

r is the yearly rate: 5% is 0.05.

PMT = $1,000 each time, r = 5% = 0.05

n is how many times a year: once.

t is the time: 10 years.

n = 1 a year, t = 10 years

2 Per payment

Interest is added each year.

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

0.05 divided by 1 is 0.05.

i = rn = 0.051 = 0.05

i = the rate each year

And N is how many deposits: 1 times 10 is 10.

N = n × t = 1 × 10 = 10

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 0.05 is 1.05.

FV = 1000 × 1.05¹⁰ − 10.05

4 Work it out

With a calculator, 1.05 to the power 10 is about 1.62889.

Minus 1, divided by 0.05: about 12.5779.

1.05¹⁰ ≈ 1.62889

(1.62889 − 1) ÷ 0.05 ≈ 12.5779

So FV is 1000 times 12.5779.

FV ≈ 1000 × 12.5779

Money is rounded to cents: about 12577 dollars and 89 cents.

FV ≈ $12,577.89

Careful!

That is only the money put in.

It leaves out all the interest.

Careful: not $1,000 × 10 ✗

5 Check

Let's check.

The deposits alone are 1000 times 10: $10000.

The account has more, because of the interest.

deposits: $1,000 × 10 = $10,000 < $12,577.89

The interest earned is 2577 dollars and 89 cents.

So it makes sense!

interest: $12,577.89 − $10,000 = $2,577.89

Let's look back.

First: read the numbers.

Then: per payment.

Then: use the formula.

Then: work it out.

Last: check.

Answer