Question 1162472
A- A company borrowed $ 74,500. The company plans to set up a sinking fund that will pay back the loan at the end of 6 years. Assuming a rate of 6% compounded semiannually, find the Sinking Fund of the ordinary annuity.


assuming you invest a certain amount of money at the end of each half year, a financial calculator, such as the TI-BA-II, will tell you that you would have to invest 7,484.43 at the end of each half year.
your inputs would be:
present value = 74,500
future value = 0
interest rate per half year = 6% per year / 2 = 3% per half year.
number of half years = 6 years * 2 = 12 half years.
your output would be the 7,484.43 mentioned above.
the sum of your payments would be 12 * 7,484.43 = 89,813.16.
the total interest payments would be that minus 74,500 = 15,313.16.
the payment at the end of each half year has been rounded to the nearest penny.


B- An employee decided to invest $ 1,960 quarterly for eight years in an ordinary annuity at 20%. What is the total cash value of the annuity at end of year 8?


a financial calculator, such as the TI-BA-II, will tell you that you would have 147,585.71 at the end of the 8 year period.
your inputs to this calculator would be:
present value = 0
future value = 0
payments made at the end of each quarter would be 1960.
interest rate per quarter would be 20% per year / 4 = 5% each quarter.
number of payments would be 8 years * 4 quarter per year = 32 quarters.


C- What must YOU invest today to receive an annuity of $ 3,800 for 12 years compounded at 8% quarterly when all withdrawals will be made at the end of each period?


a financial calculator, such as the TI-BA-II, will tell you that you would need to invest 116,557.85 now in order to be able to have 3800 available at the end of each quarter in 8 years time from now.
your inputs to this calculator would be:
present value = 0
future value = 0
number of quarters = 12 years * 4 = 48
interest rate per quarter would be 8% per year / 4 = 2% per quarter.


there is an online calculator that would provide you with similar results.
that calculator can be found at:


<a href = "https://arachnoid.com/finance/index.html" target = "_blank">https://arachnoid.com/finance/index.html</a>


here's the results of using that calculator.


for for problem A .....


<img src = "http://theo.x10hosting.com/2020/081001.jpg" >


for problem B .....


<img src = "http://theo.x10hosting.com/2020/081002.jpg" >


for problem C .....


<img src = "http://theo.x10hosting.com/2020/081003.jpg" >



inputs to these calculators use cash flow conventions.
money coming in is shown as positive.
money going out is shown as negative.