A rich donor gives a hospital $ 960 comma 000 one year from today. Each year after that, the hospital will receive a payment 5 % larger than the previous payment, with the last payment occurring in ten years' time. What is the present value (PV) of this donation, given that the interest rate is 9 %?

$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:

,  ............................................. (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

PV = $7,560,000

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