Answer:
$7,681,257.74
Explanation:
Since the hospital will receive a payment 6% larger than the previous payment each year after the first payment, the formula for the Present Value of a Growing Annuity is used to obtain the present value.
The present value of a growing annuity formula is meant for the estimation of the present day value different payments hat grow at a proportionate rate which will be received for a period of time. This formula is stated as follows:
PV = {P ÷ (r - g)} × {1 - [(1+g)÷(1+r)]^n] ...................................... (1)
Where
PV = Present value
P = First payment = $1,040,000
r = interest rate = 11% = 0.11
g = growth rate = 6% = 0.06
n = number of years = 10 years
Substuiting all the values into equation (1), we have:
PV = {$1,040,000 ÷ (0.11 - 0.06)} × {1 - [(1+0.6)÷(1+0.11)]^10]
= {$1,040,000 ÷ (0.05)} × {1 - [(1.06)÷(1.11)]^10]
= {$1,040,000 ÷ (0.05)} × {1 - [(1.06)÷(1.11)]^10]
= $20,800,000 × (1 - 0.630708763)
= $20,800,000 × 0.369291237
= $7,681,257.74
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