Answer:
$7,560,000
Explanation:
To solve this problem, the Present Value (PV) of a growing annuity formula is used.
The Present Value of a growing annuity is the current value of a series of payments which grows or diminishes at a constant rate each period.
The formula below represents the PV of a growing annuity:
[tex]PV=PMT *\frac{(1-(1+g)^{n}*(1+i)^{-n}) }{i-g}[/tex], ............................................. (i)
where,
PV = Present Value = ?
PMT = Periodic Payment = $960,000
i = Interest Rate = 9% = 0.09
g = Growth Rate = 5% = 0.05
n = Number of periods = 10 years
Substituting these values in equation (i), we have
[tex]PV=960000*\frac{(1-(1+0.05)^{10}*(1+0.09)^{-10} }{0.09-0.05}[/tex]
[tex]PV=960000*\frac{(1-(1.05^{10})*(1.09)^{-10}) }{0.04}[/tex]
[tex]PV=960000*\frac{(1-(1.63*0.42))}{0.04}[/tex]
[tex]PV=960000*\frac{(1-0.685)}{0.04}[/tex]
[tex]PV=960000*\frac{0.315}{0.04}[/tex]
[tex]PV=960000*7.875[/tex]
[tex]PV=$7,560,000[/tex]
PV = $7,560,000
