document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198081>Question 1198081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following table shows the average life expectancies in several countries. Assume that all premiums you calculate are based on end-of-month deposits in a fund yielding 6.8% annual interest compounded monthly to be paid out when a person reaches the life expectancy. HINT [See Example 2.]<BR>\n" );
document.write( "Country	Japan	Canada	U.K.	U.S.	Mexico	China	India<BR>\n" );
document.write( "Life<BR>\n" );
document.write( "Expectancy:<BR>\n" );
document.write( "Male	80	80	79	76	73	74	64<BR>\n" );
document.write( "Life<BR>\n" );
document.write( "Expectancy:<BR>\n" );
document.write( "Female	87	84	83	81	79	77	68<BR>\n" );
document.write( "Calculate the life insurance monthly premium that a 50-year-old female in Japan would pay for a $10,000,000 policy. (Round your answer to the nearest cent.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848346 by </B><A HREF=/tutors/aboutme.mpl?userid=onyulee><B>onyulee(41)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onyulee><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=848346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Determine the Number of Months**\r<BR>\n" );
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document.write( "* Life expectancy for a 50-year-old female in Japan: 87 years<BR>\n" );
document.write( "* Years to live: 87 years - 50 years = 37 years<BR>\n" );
document.write( "* Number of months to live: 37 years * 12 months/year = 444 months\r<BR>\n" );
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document.write( "**2. Calculate the Monthly Interest Rate**\r<BR>\n" );
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document.write( "* Annual interest rate: 6.8%<BR>\n" );
document.write( "* Monthly interest rate: 6.8% / 12 = 0.5667%\r<BR>\n" );
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document.write( "**3. Calculate the Future Value of a Single Deposit**\r<BR>\n" );
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document.write( "* We need to find the future value of a single deposit that will grow to $10,000,000 in 444 months.<BR>\n" );
document.write( "* Use the future value of an ordinary annuity formula:\r<BR>\n" );
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document.write( "   * FV = P * [(1 + r)^n - 1] / r \r<BR>\n" );
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document.write( "   * Where:<BR>\n" );
document.write( "      * FV = Future Value ($10,000,000)<BR>\n" );
document.write( "      * P = Monthly Premium (unknown)<BR>\n" );
document.write( "      * r = Monthly interest rate (0.005667)<BR>\n" );
document.write( "      * n = Number of months (444)\r<BR>\n" );
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document.write( "**4. Solve for the Monthly Premium (P)**\r<BR>\n" );
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document.write( "* Rearrange the formula to solve for P:\r<BR>\n" );
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document.write( "   * P = FV * [r / ((1 + r)^n - 1)]\r<BR>\n" );
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document.write( "* Substitute the values:\r<BR>\n" );
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document.write( "   * P = $10,000,000 * [0.005667 / ((1 + 0.005667)^444 - 1)]\r<BR>\n" );
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document.write( "* Calculate P:\r<BR>\n" );
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document.write( "   * P ≈ $10,000,000 * [0.005667 / (15.236 - 1)] <BR>\n" );
document.write( "   * P ≈ $10,000,000 * [0.005667 / 14.236]<BR>\n" );
document.write( "   * P ≈ $10,000,000 * 0.000398<BR>\n" );
document.write( "   * P ≈ $3,980\r<BR>\n" );
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document.write( "**Therefore, the monthly premium for a 50-year-old female in Japan for a $10,000,000 life insurance policy would be approximately $3,980.**\r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* This calculation assumes that the interest rate remains constant over the entire 37-year period, which may not be the case in reality. <BR>\n" );
document.write( "* This calculation also assumes that the individual lives exactly to the life expectancy. <BR>\n" );
document.write( "* This is a simplified model and actual life insurance premiums are determined by various factors, including health, lifestyle, and other risk factors.\r<BR>\n" );
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document.write( "This information is for illustrative purposes only and does not constitute financial advice. Please consult with a qualified financial advisor for personalized guidance.<BR>\n" );
document.write( " </SPAN>\n" );
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