According to one​ study, the average monthly cell phone bill in a certain country is ​$80 ​(up 31% since​ 2009). If an 18​-year old student with an average bill gives up his cell phone and each month invests the ​$80 he would have spent on his phone bill in a savings plan that averages a 3​% annual​ return, how much will he have saved by the time he is 60​?
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Part 1
He will have saved ​$
  
enter your response here by the time he is 60.
​(Round to the nearest cent as​ needed.) 

To determine how much the student will have saved by the time he is 60, we need to use the formula for the future value of a series of monthly investments with compound interest. The formula is:

\[
FV = P \times \frac{{(1 + r/n)^{nt} - 1}}{{r/n}}
\]

Where:
- $FV$ is the future value (the total amount saved)
- $P$ is the monthly investment ($80 in this case)
- $r$ is the annual interest rate (3%, or 0.03)
- $n$ is the number of times the interest is compounded per year (since the investment is monthly, $n = 12$)
- $t$ is the number of years (from age 18 to age 60, so $t = 60 - 18 = 42$)

Now, let's calculate this. I'll plug in the values and compute the future value.By the time the student is 60 years old, he will have saved approximately **$80,636.24**.

Would you like more details or have any questions? Here are 5 related questions you might explore:

1. How would the total savings change with a 5% annual return instead of 3%?
2. What if the student invested $100 per month instead of $80?
3. How much would the student save if the investment period was only 30 years instead of 42?
4. How does compounding monthly compare to compounding quarterly in this case?
5. What is the total interest earned during the investment period?

**Tip**: The earlier you start investing, the more you benefit from compound interest!

According to one study, the average monthly cell phone bill in a certain country is $80 (up 31% since 2009). If an 18-year old student with an average bill gives up his cell phone and each month invests the $80 he would have spent on his phone bill in a savings plan that averages a 3% annual return, how much will he have saved by the time he is 60? He will have saved $____ by the time he is 60. (Round to the nearest cent as needed.)

Discover how an 18-year-old student can save over $80,000 by the age of 60 through monthly $80 investments with a 3% annual return. This compound interest calculation illustrates savings growth over 42 years, using the formula for future value. Suitable for students in Grades 10-12.

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