Question
Jacob opened a money-market account. In the first month, he made an initial deposit of \( \$ 500 \). Starting in the second month, he plans to contribute \( \$ 75 \) a month. The account does not pay any interest. After how many months will he have a total of \( \$ 1,475 \) ?
Ask by Mullins Bates. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Jacob will have \$1,475 after 14 months.
Solution
To determine after how many months Jacob will have a total of \$1,475 in his money-market account, let's break down the contributions:
1. **Initial Deposit (Month 1):** Jacob starts with an initial deposit of \$500.
2. **Monthly Contributions (From Month 2 onward):** Starting in the second month, he contributes \$75 each month.
Let \( m \) represent the total number of months.
The total amount after \( m \) months can be calculated as:
\[
\text{Total} = \text{Initial Deposit} + \text{Monthly Contributions}
\]
\[
1475 = 500 + 75 \times (m - 1)
\]
**Solving for \( m \):**
\[
1475 = 500 + 75m - 75
\]
\[
1475 = 425 + 75m
\]
\[
1475 - 425 = 75m
\]
\[
1050 = 75m
\]
\[
m = \frac{1050}{75} = 14
\]
**Conclusion:** It will take **14 months** for Jacob to have a total of \$1,475 in his account.
**Answer:** 14
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To figure out how many months it will take Jacob to reach a total of \$1,475, we can set up an equation. He starts with an initial deposit of \$500 and will contribute \$75 every month after that. Let \( n \) represent the number of months after the initial deposit. After \( n \) months, the total amount will be: \[ \text{Total Amount} = 500 + 75n \] We want to find \( n \) when the total amount equals \$1,475: \[ 500 + 75n = 1,475 \] Subtracting 500 from both sides: \[ 75n = 975 \] Now, divide both sides by 75: \[ n = \frac{975}{75} = 13 \] So, Jacob will need a total of **13 months** to reach \$1,475 in his money-market account.
