Josh has $500 in his savings account. He deposits $25 into his savings account each month. He purchased home theater equipment for $1,600. The store he bought the equipment from offered him a $1,600 interest-free loan for 24 months. He pays off $80 of the loan every month from his checking account (not his savings account). How many months will it take for Josh to have enough money in his savings account to pay off the entire outstanding amount for his purchase? Round your answer to the nearest whole number.

We are asked to determine how many months it will take for Josh to have enough money in his savings account to pay off the entire $1,600 loan using his monthly deposits.

### Step-by-Step Breakdown:

1. **Initial Savings:**
   - Josh starts with $500 in his savings account.

2. **Monthly Deposits:**
   - He deposits $25 into his savings account every month.

3. **Loan Details:**
   - Josh purchased home theater equipment worth $1,600.
   - He is paying off $80 per month from his checking account (this does not affect his savings).
   - We are interested in how many months it will take for his savings to reach $1,600.

### Formula Setup:

Let $ x $ represent the number of months it will take for Josh to accumulate enough money in his savings account to have $1,600.

The formula to represent his savings after $ x $ months is:

\[
\text{Savings after } x \text{ months} = 500 + 25x
\]

We want to know when this amount reaches $1,600:

\[
500 + 25x = 1600
\]

### Solve for $ x $:

1. Subtract 500 from both sides:

\[
25x = 1600 - 500
\]

\[
25x = 1100
\]

2. Divide both sides by 25:

\[
x = \frac{1100}{25}
\]

\[
x = 44
\]

### Final Answer:
It will take Josh **44 months** to have enough money in his savings account to pay off the $1,600 loan.

---

Would you like further details or have any questions? Here are some related questions to deepen understanding:

1. What if Josh increased his monthly deposit to $30? How would that change the time needed?
2. How much money will Josh have left in his savings account after 24 months if he keeps making his monthly deposits?
3. What if the loan had an interest rate of 5%? How would his payments change?
4. How many months would it take for Josh to save up $2,000 if he maintains the same deposit rate?
5. How much total money will Josh have deposited into his savings account by the end of 44 months?

**Tip:** Always make sure to separate your loan repayments from your savings to avoid confusion when managing finances.

Discover how many months it will take for Josh to save enough money to pay off a $1,600 loan. This algebra problem explores linear equations and savings growth, suitable for students in Grades 6-8. Learn step-by-step how Josh accumulates savings with monthly deposits.

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