document.write( "Question 1185118: On May 11, 1993, a note due on January 10, 1994 was discounted at 12.12% simple discount. Find the exact simple interest rate of 10.75% for one year and 3 months? What is the exact discount rate? \n" ); document.write( "
Algebra.Com's Answer #849767 by CPhill(1959)\"\" \"About 
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Here's how to calculate the exact discount rate:\r
\n" ); document.write( "\n" ); document.write( "**1. Calculate the time to maturity:**\r
\n" ); document.write( "\n" ); document.write( "The note is due on January 10, 1994, and was discounted on May 11, 1993. We need to find the number of days between these two dates. Let's assume a 360-day year for simplicity (though a more precise calculation could use actual day counts).\r
\n" ); document.write( "\n" ); document.write( "From May 11, 1993, to January 10, 1994:\r
\n" ); document.write( "\n" ); document.write( "* May (31-11) = 20 days
\n" ); document.write( "* June = 30 days
\n" ); document.write( "* July = 31 days
\n" ); document.write( "* August = 31 days
\n" ); document.write( "* September = 30 days
\n" ); document.write( "* October = 31 days
\n" ); document.write( "* November = 30 days
\n" ); document.write( "* December = 31 days
\n" ); document.write( "* January = 10 days\r
\n" ); document.write( "\n" ); document.write( "Total days = 20 + 30 + 31 + 31 + 30 + 31 + 30 + 31 + 10 = 244 days\r
\n" ); document.write( "\n" ); document.write( "**2. Calculate the discount:**\r
\n" ); document.write( "\n" ); document.write( "Discount rate = 12.12% = 0.1212\r
\n" ); document.write( "\n" ); document.write( "Discount = Discount rate * Time to maturity (in years)
\n" ); document.write( "Discount = 0.1212 * (244/360) ≈ 0.0818\r
\n" ); document.write( "\n" ); document.write( "**3. Calculate the equivalent simple interest rate:**\r
\n" ); document.write( "\n" ); document.write( "Let 'i' be the equivalent simple interest rate. The relationship between simple interest and simple discount is given by:\r
\n" ); document.write( "\n" ); document.write( "Discount = (Principal * Discount Rate * Time) / (1 + i * Time)
\n" ); document.write( "We can simplify this if we assume a principal of $1 to make the calculation easier:\r
\n" ); document.write( "\n" ); document.write( "0.0818 = (1 * 0.1212 * (244/360)) / (1 + i * (244/360))
\n" ); document.write( "Solving for 'i' we get:
\n" ); document.write( "i ≈ 0.1344 or 13.44%\r
\n" ); document.write( "\n" ); document.write( "**4. Calculate the exact discount rate for one year and 3 months:**\r
\n" ); document.write( "\n" ); document.write( "One year and three months is equivalent to 15 months. Assuming 30 days per month, this would be 15 * 30 = 450 days.\r
\n" ); document.write( "\n" ); document.write( "Exact simple interest rate = 10.75% = 0.1075\r
\n" ); document.write( "\n" ); document.write( "Exact discount rate = (i * t) / (1 + i * t)
\n" ); document.write( "Where i is the interest rate and t is the time in years.
\n" ); document.write( "Exact discount rate = (0.1075 * (450/360)) / (1 + 0.1075 * (450/360))
\n" ); document.write( "Exact discount rate = 0.1344 or 13.44%\r
\n" ); document.write( "\n" ); document.write( "**Therefore:**\r
\n" ); document.write( "\n" ); document.write( "* The equivalent simple interest rate is approximately 13.44%.
\n" ); document.write( "* The exact discount rate for one year and three months at 10.75% simple interest is 13.44%.
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