Question 1119012
the future value of your investment of 21,962.68 at the end of every 6 month period for 10 years is equal to $590,145.44, according to the results of the financial calculator i used at <a href = "https://arachnoid.com/finance/" target = "_blank">https://arachnoid.com/finance/</a>


that is the just enough to pay off your debt at that time.


the future value of your debt at 7% per year compounded anually is equal to x * 1.07^10 = 1.967151357 * x.


therefore 1.967151357 * x = 590,145.44.


solve for x to get x = 590,145.44 / 1.967151357 = 300,000.0167.


this can be rounded to 300,000 dollars, which should be your answer.


the future value of your debt of 300,000.0167 today is equal to 300,000.0167 * 1.07 ^ 10 = 590145.44.


the future value of your semi-annual payments into the sinking fund is exactly equal to that as shown in the following printout.


<img src = "http://theo.x10hosting.com/2018/062501.jpg" alt = "$$$" >


the inputs to that calculator were:


present value = 0
number of time periods = 10 years * 2 payments per year = 20 semi-annual time periods.
the payment made at the end of each semi-annual period is 21962.68.
the interest rate per time period is 6% per year / 2 semi-annual periods per year = 3% per semi-annual time period.
the payments are made at the end of each semi-annual time period.


the output of that calculator is:


future value = 590,145.44.