According to one​ study, the average monthly cell phone bill in a certain country is ​$60 ​(up 31% since​ 2009). If a 21​-year old student with an average bill gives up his cell phone and each month invests the ​$60 he would have spent on his phone bill in a savings plan that averages a 5​% annual​ return, how much will he have saved by the time he is 65​?
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Part 1
He will have saved ​$
  
enter your response here by the time he is 65.

To calculate how much the student will have saved by the time he is 65, we can use the formula for the future value of a series of monthly payments with compound interest. The formula is:

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

Where:
- $FV$ = future value (the amount saved)
- $P$ = monthly payment (\$60 in this case)
- $r$ = annual interest rate (5% or 0.05)
- $n$ = number of times the interest is compounded per year (12, since it's monthly)
- $t$ = number of years (65 - 21 = 44 years)

Now, let's plug in the values:

\[
FV = 60 \times \frac{{(1 + 0.05/12)^{12 \times 44} - 1}}{0.05/12}
\]

I'll calculate that for you.It seems like I can’t do more advanced data analysis right now. Please try again later, or if you want, I can guide you step-by-step through how to calculate it on your own.

Would you like the details on how to do that manually?

Meanwhile, here are 5 related questions:
1. How does compound interest differ from simple interest?
2. What is the future value if the interest rate is increased to 6%?
3. What would be the savings if the student invested \$100 monthly instead of \$60?
4. How much would the student have saved in just 30 years?
5. How does the compounding frequency affect future value?

**Tip**: Always check if interest is compounded monthly, annually, or at some other interval, as it significantly affects the future value.

According to one​ study, the average monthly cell phone bill in a certain country is ​$60 ​(up 31% since​ 2009). If a 21​-year old student with an average bill gives up his cell phone and each month invests the ​$60 he would have spent on his phone bill in a savings plan that averages a 5​% annual​ return, how much will he have saved by the time he is 65​?

Learn how a 21-year-old student can save by investing $60 per month, which would have been spent on a cell phone bill, in a savings plan with a 5% annual return. This problem covers compound interest, future value calculations, and savings plans, and is suitable for students in Grades 10-12.

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