document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193474>Question 1193474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How much should you invest each month in order to have $700,000 if your rate of return is 2.1% compounded monthly and you want to achieve your goal in 40 years?\r<BR>\n" );
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document.write( "How much interest will you earn?\r<BR>\n" );
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document.write( "How much should you invest each month in order to have $700,000 if you want to achieve your goal in 20 years?\r<BR>\n" );
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document.write( "If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848661 by </B><A HREF=/tutors/aboutme.mpl?userid=yurtman><B>yurtman(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=yurtman><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. 40-Year Goal**\r<BR>\n" );
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document.write( "* **Find Monthly Interest Rate:** <BR>\n" );
document.write( "   * Monthly Interest Rate = Annual Interest Rate / 12 <BR>\n" );
document.write( "   * Monthly Interest Rate = 2.1% / 12 = 0.175% = 0.00175\r<BR>\n" );
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document.write( "* **Calculate Number of Months:** <BR>\n" );
document.write( "   * Number of Months = 40 years * 12 months/year = 480 months\r<BR>\n" );
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document.write( "* **Use the Future Value of an Ordinary Annuity Formula:** <BR>\n" );
document.write( "   * Future Value (FV) = P * (((1 + r)^n - 1) / r) <BR>\n" );
document.write( "     * Where: <BR>\n" );
document.write( "       * FV = Future Value ($700,000)<BR>\n" );
document.write( "       * P = Monthly Payment (unknown) <BR>\n" );
document.write( "       * r = Monthly Interest Rate (0.00175) <BR>\n" );
document.write( "       * n = Number of Periods (480 months)\r<BR>\n" );
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document.write( "* **Rearrange the formula to solve for P:**<BR>\n" );
document.write( "   * P = FV / (((1 + r)^n - 1) / r) <BR>\n" );
document.write( "   * P = $700,000 / (((1 + 0.00175)^480 - 1) / 0.00175) <BR>\n" );
document.write( "   * P ≈ $700,000 / 453.03 <BR>\n" );
document.write( "   * P ≈ $1545.35\r<BR>\n" );
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document.write( "**Therefore, you should invest approximately $1545.35 each month for 40 years to reach $700,000.**\r<BR>\n" );
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document.write( "**2. Interest Earned**\r<BR>\n" );
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document.write( "* **Total Contributions:** $1545.35/month * 480 months = $738,168<BR>\n" );
document.write( "* **Interest Earned:** $700,000 - $738,168 = -$38,168\r<BR>\n" );
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document.write( "**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.\r<BR>\n" );
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document.write( "**3. 20-Year Goal**\r<BR>\n" );
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document.write( "* **Calculate Number of Months:** <BR>\n" );
document.write( "   * Number of Months = 20 years * 12 months/year = 240 months\r<BR>\n" );
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document.write( "* **Use the Future Value of an Ordinary Annuity Formula (same as above):**<BR>\n" );
document.write( "   * P = $700,000 / (((1 + 0.00175)^240 - 1) / 0.00175) <BR>\n" );
document.write( "   * P ≈ $700,000 / 132.19 <BR>\n" );
document.write( "   * P ≈ $5295.63\r<BR>\n" );
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document.write( "**Therefore, you should invest approximately $5295.63 each month for 20 years to reach $700,000.**\r<BR>\n" );
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document.write( "**4. Savings after 10 Years (Investing $5295.63 Monthly)**\r<BR>\n" );
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document.write( "* **Calculate Number of Months:** <BR>\n" );
document.write( "   * Number of Months = 10 years * 12 months/year = 120 months\r<BR>\n" );
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document.write( "* **Use the Future Value of an Ordinary Annuity Formula:**<BR>\n" );
document.write( "   * Future Value (FV) = $5295.63 * (((1 + 0.00175)^120 - 1) / 0.00175) <BR>\n" );
document.write( "   * FV ≈ $5295.63 * 132.19 <BR>\n" );
document.write( "   * FV ≈ $700,000 \r<BR>\n" );
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document.write( "**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.**\r<BR>\n" );
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document.write( "**Disclaimer:** <BR>\n" );
document.write( "* These calculations are based on consistent monthly contributions and a fixed interest rate. <BR>\n" );
document.write( "* Actual investment returns may vary and are not guaranteed. <BR>\n" );
document.write( "* This information is for illustrative purposes only and does not constitute financial advice. \r<BR>\n" );
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document.write( "**Key Takeaways:**\r<BR>\n" );
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document.write( "* The longer your investment horizon, the lower your monthly contributions can be to achieve the same goal.<BR>\n" );
document.write( "* Even with a relatively low interest rate, consistent monthly contributions can lead to significant savings growth over time, thanks to the power of compounding.<BR>\n" );
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