$1000 grows by 5% a year. How much is it after 3 years?

Step by step

The question

Question: $1000 grows by 5% a year.

How much is it after 3 years?

1 Find the start and the factor

The start is $1000.

Each year it keeps all of it, 100%, and gets 5% more.

So it becomes 105% of what it was.

105% is 1.05.

That is the factor.

2 Write the rule

x is the number of years.

Each year we multiply by 1.05 again.

So y = 1000 × 1.05ˣ.

Careful!

The 5% is taken of the NEW amount every year, not always of $1000.

3 Put in x = 3

After 3 years, x = 3.

1.05 to the power 3 is 1.157625 (with a calculator).

So we multiply 1000 by 1.157625.

That is 1157.625.

Money is rounded to cents: about $1157.63.

4 Check

Let's check year by year.

We start at $1000, and multiply by 1.05 each year.

After 3 years we get 1157.625 again.

It works!

Let's look back.

First: find the start and the factor.

Then: write the rule.

Then: put in x = 3.

Last: check.