Question 1119012: A debt of x, with interest rate of 7% compounded annually will be retired at the end of 10 years through the accumulation of deposit in the sinking fund invested at 6% compounded semi-annually. The deposit in the sinking fund every end of six months is 21,962.68. What is the value of x?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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 https://arachnoid.com/finance/
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.
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.
|
|
|
