An investor has a quarterly compounded required rate of return of 9% per year. How much will he pay for a nine-year ordinary annuity that pays $100 per year?
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A. B. C. D.C
The annually compounded rate equals (1 + 9%/4)^4 - 1 = 9.3%. Therefore, the present value of the annuity equals 100/0.093*[1 - 1/1.093^9] = $592.6.
To calculate the price of an ordinary annuity, we can use the formula:
PV=C×(1−(1+r)−n)/r
where: PV = Present value of the annuity C = Cash flow per period (in this case, $100 per year) r = Required rate of return per period (quarterly compounded rate) n = Number of periods (in this case, 9 years)
Let's calculate the present value (PV) using the given information:
First, we need to convert the annual rate of return to a quarterly rate by dividing it by 4: r=9%/4=0.09/4=0.0225
Now, we can substitute the values into the formula and solve for PV: PV=100×(1−(1+0.0225)−9×4)/0.0225
Calculating this expression: PV=100×(1−1.0225−36)/0.0225 PV=100×(1−0.5960)/0.0225 PV=100×0.4040/0.0225 PV=4040/0.0225 PV=179,555.56
Therefore, the investor should pay approximately $179,555.56 for the nine-year ordinary annuity that pays $100 per year.
None of the provided answer options match the calculated value exactly.