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

77​%

annual​ return, how much will

hehe

have saved by the time

hehe

is

7070​?

Question content area bottom

Part 1

HeHe

will have saved

​$enter your response here

by the time

hehe

is

7070.

To calculate how much the 19-year-old student will have saved by the time he is 70 years old, we will use the **future value of an annuity formula**. This formula is used when someone makes regular investments and those investments grow at a certain interest rate.

### Future Value of an Annuity Formula:
\[
FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]
Where:
- $FV$ = Future Value (the total amount saved)
- $P$ = Monthly investment (\$40 in this case)
- $r$ = Monthly interest rate (7% annually, which is $ \frac{7}{12} \approx 0.005833 $ per month)
- $n$ = Total number of months (from age 19 to 70, which is $51 \times 12 = 612$ months)

Now let's plug in the values and calculate.

\[
FV = 40 \times \left( \frac{(1 + 0.005833)^{612} - 1}{0.005833} \right)
\]

Let me calculate the future value for you.By the time the student is 70 years old, he will have saved approximately **$234,172.20** by investing $40 each month in a plan with a 7% annual return.

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

Here are 5 related questions to expand on this topic:
1. What is the impact of increasing the monthly savings amount on the final value?
2. How would a change in the annual interest rate affect the future savings?
3. What if the student starts saving at a different age?
4. How much would the student save if the interest was compounded quarterly instead of monthly?
5. What if the student paused saving for a few years; how would that affect the result?

**Tip**: Even small monthly investments can grow significantly over time due to compound interest. The earlier you start, the more you benefit!

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 7% annual return, how much will he have saved by the time he is 70?

Discover how a 19-year-old student can save $234,172.20 by investing $40 per month in a savings plan with a 7% annual return over 51 years. This problem demonstrates the power of compound interest and the future value of an annuity formula. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation