A 180 day promissory note dated September 14th, 2010 is made at 5.25% for $1665. What...

A 180 day promissory note dated September 14^th, 2010 is made at 5.25% for $1665. What are the proceeds of the note if it is sold on December 9^th , 2010 and money is worth 6% simple interest?

Use six decimal places for any intermediate calculations and round the final answer to 2 decimal places. (e.g., 0.00)

Solutions

Expert Solution

Days to maturity of promissory note = 180 | Issue Date = 14th September 2010 | Rate of interest = 5.25%

Principal = $1,665

First we will calculate the maturity value of the note after 180 days.

Date of maturity = Issue Date + 180 days = 14th September 2010 + 180 = 13th March 2011

Using simple inerest, we can calculate the Value of note at maturity.

Value of note at maturity = Principal * (1 + Rate of interest * Time)

Time in year = Number of days to maturity / 365 = 180 / 365

Value of note at maturity = 1,665 * (1 + 5.25% * 180 / 365) = 1,665 * 1.02589

Value of note at maturity = $1,708.11

Now the note is sold on December 9th 2010 at 6% interest rate.

Time remaining to maturity = Maturity date - Date of selling = 13th March 2011 - December 9th 2010

Time remaining to maturity = 94 days

We need to find the price that we would get if the note is sold on December 9th 2010. Therefore, we will find the Present worth of Future Value we calculated earlier with 180 maturity days.

To find the Present worth, we will use Simple interest formula, where Principal is unknown however, Value of note is known.

Simple Interest formula: Value of note at maturity = Principal * (1 + Rate of interest * Time)

Reversing the formula to solve for Principal.

Principal = Value at maturity / ( 1 + Rate of interest * Time)

Time = Number of days remaining to maturity / 365 = 94 / 365

=> P = 1,708.11 / (1 + 6% * 94 / 365) = 1,708.11 / 1.0155

Proceeds if note is sold on December 9th 2010 = 1,682.12

Hence, Present worth of Promissory note on December 9th 2010 is 1,682.12

jeff jeffy answered 1 year ago

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