1. An aunt wishes to pass on some of her wealth to her nieces and nephews. She decides to give each a perpetuity that pays $36,000 per year starting a year from now and increasing by 2% per annum. How much will she have to set aside for each child? Use a discount rate of 5%.
2. At age 25, Robert decides to save $4,000 per year (starting a year from now) for each of the next 10 years and save nothing thereafter. How much will he have accumulated at age 65 if he is earning a stated rate of 5.0% p.a.? [Interest accrues at 5% p.a. on the balance he has accumulated after he stops adding funds.]
3. A recent Powerball jackpot was announced at $380 million payable in 30 equal annual payments over 29 years. The winner has the option of receiving 1/30th of the jackpot each year, starting immediately, or a lump sum cash option of $256.8 million. What rate of discount was used to calculate the value of the cash option?