Question

Emma has 2000 dollars in a savings account that earns 4% interest every year. she plans to keep her money in there for 5 years
if she decides to withdraw the money 2 years earlier than planned, how much interest will she have earned by then?

Answer 1

To calculate the amount of interest Emma will earn by withdrawing her money after 3 years instead of 5 years, we can use the formula for simple interest:

\[
A = P(1 + rt)
\]

Where:
- \(A\) is the amount of money accumulated after \(t\) years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(t\) is the time the money is invested or borrowed for, in years.

In Emma's case:
- \(P = 2000\) dollars
- \(r = 0.04\) (4% interest)
- \(t = 3\) years (since she withdraws 2 years earlier)

Now, substituting these values into the formula:

\[
A = 2000(1 + 0.04 \times 3)
\]
\[
A = 2000(1 + 0.12)
\]
\[
A = 2000 \times 1.12
\]
\[
A = 2240
\]

The total amount after 3 years is 2240 dollars. To find out how much interest Emma earned, we subtract the principal from the total amount:

\[
\text{Interest} = A - P = 2240 - 2000 = 240
\]

So, if Emma decides to withdraw her money 2 years earlier than planned, she will have earned **240 dollars** in interest.