According to one​ study, the average monthly cell phone bill in a certain country is 

​$4040 

​(up 31% since​ 2009). If 

aa 

1919​-year 

old student with an average bill gives up 

hishis 

cell phone and each month invests the 

​$4040 

hehe 

would have spent on 

hishis 

phone bill in a savings plan that averages a 

66​% 

annual​ return, how much will 

hehe 

have saved by the time 

hehe 

is 

5555​?

Question content area bottom

Part 1

He 

will have saved 

​$enter your response here 

by the time 

he 

is 

55

To calculate how much the student will have saved by the time he is 55, we can use the **future value of an investment formula** with regular monthly contributions and compound interest:

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

Where:
- $ A $ is the future value (the amount saved by age 55),
- $ P $ is the monthly investment (in this case, $4040),
- $ r $ is the monthly interest rate (annual interest rate divided by 12),
- $ n $ is the number of months over which the investment is made (the difference between age 55 and 19, in months).

### Step-by-Step:

1. **Monthly investment ($ P $)**: 4040 dollars.
2. **Annual interest rate**: 6%. Convert this to a monthly interest rate:
   \[
   r = \frac{6}{100} \div 12 = 0.005
   \]
3. **Duration of the investment**: From age 19 to age 55, which is $ 55 - 19 = 36 $ years. In months:
   \[
   n = 36 \times 12 = 432 \text{ months}
   \]

Now, let's plug these values into the future value formula to calculate how much he will have saved.By the time he is 55, the student will have saved approximately **$6,191,475.62**.

Would you like further details on how the formula works or any clarification?

Here are 5 related questions you might find helpful:
1. What is the impact of a higher annual return on the total savings?
2. How would saving for a shorter or longer period (e.g., 30 or 40 years) affect the total savings?
3. What would happen if the monthly contribution varied over time?
4. How does compound interest differ from simple interest in this scenario?
5. How would inflation impact the real value of the savings over time?

**Tip:** Regular contributions to a savings plan with compound interest grow significantly over time due to the power of compound growth. Starting early helps maximize returns.

According to one study, the average monthly cell phone bill in a certain country is $40 (up 31% since 2009). If a 19-year-old student with an average bill gives up his cell phone and each month invests the $40 he would have spent on his phone bill in a savings plan that averages a 6% annual return, how much will he have saved by the time he is 55?

Learn how a 19-year-old student can save $6,191,475.62 by investing $40 monthly in a savings plan with a 6% annual return. This compound interest problem involves calculating future value with regular monthly contributions. Suitable for students in Grades 9-12.

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