If an investor who has a required rate of return of 7% per year pays $1,000 for a five-year ordinary annuity, the annuity pays ________ per year.
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A. B. C. D.A
If the annuity pays C per year, we have 1,000 = C/0.07*(1-1/(1.07^5)) => C = 1,000*0.07/0.287 = 244.
To determine the annual payment of the ordinary annuity, we need to use the present value of an ordinary annuity formula. The formula is as follows:
PV=C×(1−(1+r)−n)/r
Where: PV = Present value or the initial investment ($1,000 in this case) C = Annual payment r = Required rate of return per year (7% or 0.07) n = Number of years (5 years in this case)
We need to solve the formula for C, which represents the annual payment. Rearranging the formula to solve for C, we get:
C=PV×r/(1−(1+r)−n)
Now, let's substitute the given values into the formula:
C = $1,000 \times 0.07 / \left(1 - \left(1 + 0.07\right)^{-5}\right)
Calculating the denominator:
1−(1+0.07)−5=1−1.40255=−0.40255
Since the denominator is negative, we need to take its absolute value:
∣−0.40255∣=0.40255
Now, let's substitute the value back into the formula:
C = $1,000 \times 0.07 / 0.40255
Simplifying the equation:
C = $1,000 \times 0.1739
Calculating the value:
C = $173.90
Therefore, the annual payment of the ordinary annuity is $173.90. However, none of the provided answer choices match this result. It's possible that there is an error in the answer choices or in the question itself.