Questions: According to one study, the average monthly cell phone bill in a certain country is 70 (up 31% since 2009). If a 22-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 5% annual return, how much will she have saved by the time she is 60? She will have saved by the time she is 60. (Round to the nearest cent as needed.)

According to one study, the average monthly cell phone bill in a certain country is 70 (up 31% since 2009). If a 22-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 5% annual return, how much will she have saved by the time she is 60?

She will have saved by the time she is 60. (Round to the nearest cent as needed.)

Transcript text: Points: 0 of 1 According to one study, the average monthly cell phone bill in a certain country is $\$ 70$ (up $31 \%$ since 2009). If a 22 -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 $5 \%$ annual return, how much will she have saved by the time she is 60 ? She will have saved \$ $\square$ by the time sheis 60. (Round to the nearest cent as needed.)

Solution

Solution Steps

Step 1: Identify the Parameters

The monthly investment amount (P) is $70, the annual return rate (r) is 5%, the number of compounding periods per year (n) is 12, and the total number of years (t) is 38 years, from age 22 to 60.

Step 2: Apply the Future Value of an Annuity Formula

The future value of a series of equal monthly investments is calculated using the formula: $$ FV = P \times \left( \frac{(1 + \frac{r}{n})^{n \times t} - 1}{\frac{r}{n}} \right) $$ Substituting the given values into the formula, we get: $$ FV = $70 \times \left( \frac{(1 + 0.00417)^{12 \times 38} - 1}{0.00417} \right) $$

Step 3: Perform the Calculation

After performing the calculation, the future value of the annuity is approximately $95080.52.