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

​$8080 

​(up 31% since​ 2009). If 

aa 

2222​-year 

old student with an average bill gives up 

hishis 

cell phone and each month invests the 

​$8080 

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 

6060​?

Question content area bottom

Part 1

HeHe 

will have saved 

​$enter your response here 

by the time 

hehe 

is 

6060.

​(Round to the nearest cent as​ needed.) 

To solve this problem, we need to calculate the future value of the monthly investments using compound interest.

Here are the steps:

### Formula:
The future value (FV) of an investment with regular monthly contributions can be calculated using the following formula:

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

Where:
- $P$ is the monthly investment (in this case, \$80).
- $r$ is the annual interest rate (in this case, 6%, or 0.06).
- $n$ is the number of times interest is compounded per year (since the investment is monthly, $n = 12$).
- $t$ is the time in years (from age 22 to 60, which is 38 years).
  
Now let's compute the future value.

### Variables:
- $P = 80$
- $r = 0.06$
- $n = 12$
- $t = 60 - 22 = 38$

I'll calculate the future value based on these inputs.By the time the student is 60 years old, they will have saved **$140,238.44**.

Would you like further details on the calculation or have any questions?

Here are 5 related questions you might find useful:
1. How does compounding frequency affect the future value of an investment?
2. What happens if the interest rate changes over time?
3. How does delaying the start of investments impact savings over time?
4. What would be the future value if the annual return were 8% instead of 6%?
5. How does inflation affect the real value of savings in this scenario?

**Tip:** Starting investments early and contributing regularly allows compounding to work more effectively, growing your savings over time.

According to one​ study, the average monthly cell phone bill in a certain country is $80 (up 31% since​ 2009). If a 22​-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 6​% annual return, how much will he have saved by the time he is 60​? (Round to the nearest cent as needed.)

Learn how to calculate the future value of monthly investments using compound interest. A 22-year-old student invests $80 per month with a 6% annual return and saves over 38 years. Detailed steps, including formulas and concepts, are provided. 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