Arich donor gives a hospital $100,000 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%?

a) $772,173.49
b) $585,987.27
c) $467,922.22
d) $779,843.27

D) $779,843.27

Explanation:

The present value of this donation = Donation in Year 1/(1+ discount rate)^9 + Donation in Year 2/(1+ discount rate)^8 + ….. + Donation in Year 2/(1+ discount rate)^1

= $100,000/(1+9%) + $100,000*(1+5%)/(1+9%)^2 +$100,000*(1+5%)^2/(1+9%)^3…. +$100,000*(1+5%)^9/(1+9%)^10 = $779,843.27

Or we can easily input in excel and generate NPV as file attached; in which the formula is NPV(discount rate, cash inflow year 1 : cash inflow year 10) = (9%, 100000,100000*(1+5%)….,100000*(1+5%)^9) = $779,843.27