A rich 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%?

Question

Quizplus · Accepted Answer

We can use the formula for present value of an annuity due to find the present value of the donation:
PV = PMT * [(1 - (1+i)^(-n))/i] * (1+i)
where PV is present value, PMT is the annual payment, i is the interest rate, and n is the number of years. However, since the first payment will be received one year from today, we need to multiply the result by (1+i) to account for one year of interest.

Using this formula, we can find the present value of the donation:
PMT = 100,000
i = 0.09
n = 10

PV = 100,000 * [(1 - (1+0.09)^(-10))/0.09] * (1+0.09)
PV = $779,843.27

Therefore, the best choice is C, with a present value of $779,843.27.

A Rich Donor Gives a Hospital $100 000 One Year