According to one​ study, the average monthly cell phone bill in a certain country is ​$70 ​(up 31% since​ 2009). If a 21​-year old student with an average bill gives up her cell phone and each month invests the ​$70 she would have spent on her phone bill in a savings plan that averages a 6​% annual​ return, how much will she have saved by the time she is 70​?
She will have saved ​$_____ by the time she is 70.
​(Round to the nearest cent as​ needed.) 

To determine how much the student will have saved by the time she is 70, we can use the formula for the future value of a series of regular payments with compound interest. The formula is:

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

Where:
- $FV$ is the future value (the total amount saved),
- $P$ is the regular monthly payment ($70 in this case),
- $r$ is the annual interest rate (6%, or 0.06),
- $n$ is the number of times the interest is compounded per year (12, since it's compounded monthly),
- $t$ is the number of years of saving (from age 21 to 70, so $t = 70 - 21 = 49$).

Let's calculate this value.By the time the student is 70, she will have saved approximately $248,888.96, assuming a 6% annual return with monthly contributions of $70.

Would you like any further details or have any questions about this?

Here are 5 related questions for further exploration:
1. How does the future value change if the interest rate increases to 7%?
2. What would the future value be if the student started saving at age 25 instead?
3. How does the future value differ if the monthly payment is increased to $100?
4. What would happen if the interest were compounded annually instead of monthly?
5. How much would the student have if she only saved until age 60?

**Tip:** Even small increases in regular contributions or the interest rate can significantly boost long-term savings due to compound interest!

According to one study, the average monthly cell phone bill in a certain country is $70 (up 31% since 2009). If a 21-year old student with an average bill gives up her cell phone and each month invests the $70 she would have spent on her phone bill in a savings plan that averages a 6% annual return, how much will she have saved by the time she is 70?

Learn how to calculate the future savings of a student who invests $70 monthly, compounded at a 6% annual rate, from age 21 to 70. This problem demonstrates the power of compound interest and the future value formula, suitable for high school students.

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