You currently earn ​$1000 per​ month, but you are expecting your earnings to rise 50​% per year. In five​ years, what should you expect to be​ earning?
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Part 1
Choose the correct answer. 
A.
In five​ years, you should expect to be earning exactly ​$3500 per month because your earnings rise 50​% per​ year, or ​$500 dollars per year. 
B.
In five​ years, you should expect to be earning less than ​$1000 per month because the 50​% increase in earnings is very small. 
C.
In five​ years, you should expect to be earning exactly ​$1000 per month because because the 50​% increase in earnings does play any effect. 
D.
In five​ years, you should expect to be earning more than ​$3500 per month because your earnings rise 50​% per​ year, which are added to the earnings of the previous month. 
E.
In five​ years, you should expect to be earning a little more than ​$1000 per month because the 50​% increase in earnings is very small. 
F.
In five​ years, you should expect to be earning less than ​$3500 per month because your earnings rise 50​% per​ year, which are subtracted from the earnings of the previous year. 

Let's break this down carefully:

You are earning $1000 per month, and your earnings are expected to increase by 50% per year. This is a compounded growth situation, where the earnings increase by 50% on the new amount each year, not just by adding a fixed dollar value.

We can use the compound interest formula to calculate your earnings after 5 years:

\[
A = P \left(1 + \frac{r}{100}\right)^t
\]

Where:
- $A$ is the amount after $t$ years,
- $P = 1000$ is the initial earnings,
- $r = 50\%$ is the rate of increase,
- $t = 5$ is the number of years.

Substitute the values into the formula:

\[
A = 1000 \left(1 + \frac{50}{100}\right)^5 = 1000 \left(1.5\right)^5
\]

\[
A = 1000 \times 7.59375 = 7593.75
\]

So, after 5 years, you should expect to be earning around **$7593.75 per month**.

Now let's analyze the answer choices:

- **A.** Incorrect. This assumes a linear increase of $500 per year, but the increase is compounded, not linear.
- **B.** Incorrect. The 50% increase is quite significant over time.
- **C.** Incorrect. The increase does have an effect, so you won't be earning the same $1000.
- **D.** **Correct.** You will be earning more than $3500 per month because the 50% increase is compounded annually.
- **E.** Incorrect. The increase is not small; it's compounded and quite significant.
- **F.** Incorrect. The earnings increase is not subtracted, it's compounded.

So, the correct answer is **D**.

Would you like more details or have any questions?

Here are five related questions to explore this topic:
1. How would the result change if the annual growth rate was 25% instead of 50%?
2. What would be the monthly earnings after 10 years under the same conditions?
3. How does compound interest differ from simple interest in growth scenarios like this?
4. What formula would you use if the earnings increased quarterly rather than annually?
5. How much total earnings would you accumulate over 5 years with the 50% increase?

**Tip:** When dealing with percentage increases over time, always check if the increase is linear or compounded, as compounded growth accelerates significantly over time.

You currently earn $1000 per month, but you are expecting your earnings to rise 50% per year. In five years, what should you expect to be earning?

Find out how to calculate expected earnings after 5 years with a 50% annual increase using the compound interest formula. Understand exponential growth and the significant impact of compounding in finance. Suitable for students in Grades 10-12.

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