Question 1193474
**1. 40-Year Goal**

* **Find Monthly Interest Rate:** 
   * Monthly Interest Rate = Annual Interest Rate / 12 
   * Monthly Interest Rate = 2.1% / 12 = 0.175% = 0.00175

* **Calculate Number of Months:** 
   * Number of Months = 40 years * 12 months/year = 480 months

* **Use the Future Value of an Ordinary Annuity Formula:** 
   * Future Value (FV) = P * (((1 + r)^n - 1) / r) 
     * Where: 
       * FV = Future Value ($700,000)
       * P = Monthly Payment (unknown) 
       * r = Monthly Interest Rate (0.00175) 
       * n = Number of Periods (480 months)

* **Rearrange the formula to solve for P:**
   * P = FV / (((1 + r)^n - 1) / r) 
   * P = $700,000 / (((1 + 0.00175)^480 - 1) / 0.00175) 
   * P ≈ $700,000 / 453.03 
   * P ≈ $1545.35

**Therefore, you should invest approximately $1545.35 each month for 40 years to reach $700,000.**

**2. Interest Earned**

* **Total Contributions:** $1545.35/month * 480 months = $738,168
* **Interest Earned:** $700,000 - $738,168 = -$38,168

**Note:** In this scenario, you would actually have contributed more than the final goal. This highlights the importance of investment growth and the power of compounding over long periods.

**3. 20-Year Goal**

* **Calculate Number of Months:** 
   * Number of Months = 20 years * 12 months/year = 240 months

* **Use the Future Value of an Ordinary Annuity Formula (same as above):**
   * P = $700,000 / (((1 + 0.00175)^240 - 1) / 0.00175) 
   * P ≈ $700,000 / 132.19 
   * P ≈ $5295.63

**Therefore, you should invest approximately $5295.63 each month for 20 years to reach $700,000.**

**4. Savings after 10 Years (Investing $5295.63 Monthly)**

* **Calculate Number of Months:** 
   * Number of Months = 10 years * 12 months/year = 120 months

* **Use the Future Value of an Ordinary Annuity Formula:**
   * Future Value (FV) = $5295.63 * (((1 + 0.00175)^120 - 1) / 0.00175) 
   * FV ≈ $5295.63 * 132.19 
   * FV ≈ $700,000 

**Therefore, if you invest $5295.63 each month for 10 years at a 2.1% monthly compounded rate, your savings will be worth approximately $700,000.**

**Disclaimer:** 
* These calculations are based on consistent monthly contributions and a fixed interest rate. 
* Actual investment returns may vary and are not guaranteed. 
* This information is for illustrative purposes only and does not constitute financial advice. 

**Key Takeaways:**

* The longer your investment horizon, the lower your monthly contributions can be to achieve the same goal.
* Even with a relatively low interest rate, consistent monthly contributions can lead to significant savings growth over time, thanks to the power of compounding.