Practice Questions Question 1: Simple Perpetuity A perpetual bond pays $500 annually and the interest rate is 4%. What is the present value of the bond? Solution: The formula for the present value of a perpetuity is: PV = P r Substitute the given values: P = 500, r = 0.04 500 PV = = 12, 500 0.04 Answer: The present value of the bond is $12,500. — Question 2: Growing Perpetuity A scholarship fund pays $1,000 annually and the payments grow by 2% per year. If the discount rate is 5%, what is the present value of the fund? Solution: The formula for a growing perpetuity is: PV = where: • P = 1, 000 (first payment), 1 P r−g • r = 0.05 (discount rate), • g = 0.02 (growth rate). Substitute the values: PV = 1, 000 1, 000 = = 33, 333.33 0.05 − 0.02 0.03 Answer: The present value of the scholarship fund is approximately $33,333.33. — Question 3: Calculating Annual Payment from Perpetuity Value An endowment is valued at $1,000,000 and the discount rate is 6%. What annual payment can this endowment sustain indefinitely? Solution: Rearrange the perpetuity formula to solve for P : P = PV · r Substitute the given values: P V = 1, 000, 000, r = 0.06 P = 1, 000, 000 · 0.06 = 60, 000 Answer: The endowment can sustain annual payments of $60,000 indefinitely. — Summary of Results: 1. Present value of perpetual bond: $12,500. 2. Present value of growing scholarship fund: $33,333.33. 3. Sustained annual payment from endowment: $60,000. 2