Determine the proceeds of a promissory note for $3,600 with interest at 6% p.a. compounded quarterly, issued September 1, 2008, due on June 1, 2014, and discounted on December 1,2010 at 8% compounded semi-annually.
Since I am a visual-minded person, I made a time graph to get the count of interest periods correct. From Sept 1, 2008 to June 1, 2014 I counted 23 quarters
Since the interest earned is 6% compounded quarterly, this will work out
Amount due on June 1, 2014 would be
3600(1.015)^23 , the quarterly rate is .06/4 = .015
= .....
but this was discounted to Dec1, 2010 , which would be 14 quarters or 7 half-years
discounted amount on Dec1, 2010
= 3600(1.015)^23 (1.04)^-7
= ....
I will let you do the button-pushing.
Check my time graph to make sure I counted correctly.
To determine the proceeds of a promissory note, we need to calculate the future value of the note at the given interest rates and discount rates.
Step 1: Calculate the future value of the note from September 1, 2008, to June 1, 2014, using compounding quarterly at 6% interest rate per annum.
We can use the formula for compound interest to calculate the future value:
Future Value (FV) = Principal amount * (1 + (interest rate / number of compounding periods))^(number of compounding periods * number of years)
Principal amount = $3,600
Interest rate = 6% per annum
Number of compounding periods per year = 4 (quarterly compounding)
Number of years = 2014 - 2008 = 6
Future Value = $3,600 * (1 + (0.06 / 4))^(4 * 6)
Future Value = $4,826.21
Step 2: Calculate the discounted value of the note on December 1, 2010, at an 8% semi-annually compounded interest rate.
We can use the formula for compound interest to calculate the present value:
Present Value (PV) = Future Value / (1 + (interest rate / number of compounding periods))^(number of compounding periods * number of years)
Future Value = $4,826.21
Interest rate = 8% per annum
Number of compounding periods per year = 2 (semi-annually compounding)
Number of years = 2010 - 2008 = 2
Present Value = $4,826.21 / (1 + (0.08 / 2))^(2 * 2)
Present Value = $4,204.72
Therefore, the proceeds of the promissory note are $4,204.72.