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.
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?
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?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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:
https://arachnoid.com/finance/index.html
here's the results of using that calculator.
for for problem A .....
for problem B .....
for problem C .....
inputs to these calculators use cash flow conventions.
money coming in is shown as positive.
money going out is shown as negative.
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