You want to buy a house in 6 years.  You just started a new job.  You have decided to save $229 per month so you will have a down payment.  You are investing in an index that you expect will earn 10.62% per year.  If you can follow this plan, how much will you have for a down payment when you are ready to buy that first house in 6 years?  Please enter your answer to the penny.

This problem involves calculating the **future value of a series of payments (annuity)**, given a constant monthly savings, a fixed rate of return, and a set time period. Let's break it down step by step using the **Future Value of an Annuity Formula**.

### **Formula for Future Value of an Annuity:**

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

where:  
- $FV$ = Future Value (the amount of money you will have)  
- $P$ = Payment amount per period = 229  
- $r$ = Monthly interest rate = $ \frac{10.62\%}{12} = \frac{0.1062}{12} = 0.00885 $  
- $n$ = Total number of payments = $6 \times 12 = 72$ months  

---

### **Step 1: Plug in the Values**  
\[
FV = 229 \times \left( \frac{(1 + 0.00885)^{72} - 1}{0.00885} \right)
\]

---

### **Step 2: Simplify the Expression**

1. Calculate $1 + 0.00885 = 1.00885$.  
2. Raise it to the 72nd power:  
   \[
   1.00885^{72} \approx 1.85093
   \]
3. Subtract 1:  
   \[
   1.85093 - 1 = 0.85093
   \]
4. Divide by 0.00885:  
   \[
   \frac{0.85093}{0.00885} \approx 96.15028
   \]

---

### **Step 3: Calculate the Future Value**

\[
FV = 229 \times 96.15028 \approx 22,019.39
\]

---

### **Final Answer**

If you save $229 per month and earn a 10.62% annual return, you will have **$22,019.39** in 6 years.

---

Would you like me to break down any part further, or explore related ideas?

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### **5 Related Questions:**
1. How would the future value change if the annual return was higher or lower?
2. What if you could increase your savings each year by 3% to account for raises at work?
3. How much would you need to save monthly to reach a goal of $30,000 in 6 years?
4. How does compounding frequency (e.g., monthly vs. yearly) affect the final amount?
5. What if you invested in a less risky portfolio with a 7% return instead?

---

### **Tip:**  
The earlier you start saving or the more frequently you save, the more compound interest can help grow your savings. Small changes in your contributions or returns can have a big impact over time.

You want to buy a house in 6 years. You just started a new job. You have decided to save $229 per month so you will have a down payment. You are investing in an index that you expect will earn 10.62% per year. If you can follow this plan, how much will you have for a down payment when you are ready to buy that first house in 6 years? Please enter your answer to the penny.

Learn how to calculate the future value of monthly savings of $229 invested at an annual return of 10.62% over 6 years. This problem applies the future value of an annuity formula, making it ideal for high school students (Grades 10-12) studying compound interest and savings plans.

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