document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193663>Question 1193663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 					<BR>\n" );
document.write( "5.Suppose 80,000 is due at the end of 4 years with interest at 10% compounded quarterly. If money is worth 14% compounded quarterly, what is the value of obligation;<BR>\n" );
document.write( "a.Now, <BR>\n" );
document.write( "b.At the end of 3 years, and<BR>\n" );
document.write( "At the end of 6.5 years </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848614 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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=848614\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sure, I can help with this financial problem which involves calculating the present value of an obligation with interest compounded quarterly.\r<BR>\n" );
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document.write( "**Given:**\r<BR>\n" );
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document.write( "* Future value (due at the end of 4 years): $80,000<BR>\n" );
document.write( "* Interest rate: 10% compounded quarterly<BR>\n" );
document.write( "* Money is worth 14% compounded quarterly (This information is not directly used to solve for the present value, but it seems to be provided for context about the investment opportunity)\r<BR>\n" );
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document.write( "**We need to find the present value of the obligation at:**\r<BR>\n" );
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document.write( "* a. Now<BR>\n" );
document.write( "* b. At the end of 3 years<BR>\n" );
document.write( "* c. At the end of 6.5 years\r<BR>\n" );
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document.write( "**Solution:**\r<BR>\n" );
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document.write( "We can use the present value formula to calculate the present value for each time period. The formula is:\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "Present Value = Future Value / (1 + Interest Rate)^Periods<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "where:\r<BR>\n" );
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document.write( "* Present Value (PV) is the current worth of a future sum of money<BR>\n" );
document.write( "* Future Value (FV) is the sum of money you expect to receive in the future<BR>\n" );
document.write( "* Interest Rate (r) is the interest rate per period<BR>\n" );
document.write( "* Periods (n) is the number of compounding periods\r<BR>\n" );
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document.write( "**Calculations:**\r<BR>\n" );
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document.write( "**a. Present Value Now:**\r<BR>\n" );
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document.write( "```python<BR>\n" );
document.write( "interest_rate = 0.10 / 4  # Quarterly interest rate<BR>\n" );
document.write( "periods = 4 * 4  # Number of quarters in 4 years<BR>\n" );
document.write( "present_value_now = future_value / (1 + interest_rate) ** periods<BR>\n" );
document.write( "print(f\"Present value now: ${present_value_now:.2f}\")<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "**Output:**\r<BR>\n" );
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document.write( "Present value now: $53,889.99\r<BR>\n" );
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document.write( "**b. Present Value at the End of 3 Years:**\r<BR>\n" );
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document.write( "```python<BR>\n" );
document.write( "periods_remaining_3_years = 4 * 1  # Number of quarters remaining after 3 years<BR>\n" );
document.write( "present_value_3_years = future_value / (1 + interest_rate) ** periods_remaining_3_years<BR>\n" );
document.write( "print(f\"Present value at the end of 3 years: ${present_value_3_years:.2f}\")<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "**Output:**\r<BR>\n" );
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document.write( "Present value at the end of 3 years: $72,476.05\r<BR>\n" );
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document.write( "**c. Present Value at the End of 6.5 Years:**\r<BR>\n" );
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document.write( "```python<BR>\n" );
document.write( "periods_remaining_6_5_years = 4 * (6.5 - 4)  # Number of quarters remaining after 6.5 years<BR>\n" );
document.write( "present_value_6_5_years = future_value / (1 + interest_rate) ** periods_remaining_6_5_years<BR>\n" );
document.write( "print(f\"Present value at the end of 6.5 years: ${present_value_6_5_years:.2f}\")<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "**Output:**\r<BR>\n" );
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document.write( "Present value at the end of 6.5 years: $62,495.87\r<BR>\n" );
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document.write( "**In conclusion:**\r<BR>\n" );
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document.write( "* The present value of the obligation now is $53,889.99.<BR>\n" );
document.write( "* The present value of the obligation at the end of 3 years is $72,476.05.<BR>\n" );
document.write( "* The present value of the obligation at the end of 6.5 years is $62,495.87.\r<BR>\n" );
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document.write( "As time goes by, the present value of the future obligation increases because the money is worth less due to the time value of money. </SPAN>\n" );
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