Challenging Problems 9. Suppose there is a security that pays you $10 every night. It will pay the first $10 on December 25 (Christmas) evening, 2020 and will pay you $10 every 7th night (meaning the next $10 on New Years Eve, 31st), forever thereafter, into perpetuity. Assume that the yearly rate of interest is 3.65%. Assume daily compounding. (Hint - this is a 7-day perpetuity) a) How much would you be willing to pay for this security on Christmas Eve, that is, a day before you get the first cash-flow of $10? b) How much would you be willing to pay for this security on the evening of November 30? 10. Suppose today is Dec 31st, 2020, and as always, today is time t=0. Prithu wants to buy a $20 million yacht. The dealer is offering the following scheme. Pay $2 million as down payment today and borrow $18 million from the dealership at 18% per year and payoff the loan in 4 yearly installments, the first installment is due one year from now, meaning December 31, 2021. If he agrees to the scheme, he will receive the delivery of the brand-new luxury yacht, exactly 2 years from today, meaning on December 31, 2022. Prithu also estimates that dockage charges, crew salary, insurance, fuel and general maintenance of the yacht that cost $1.2 million per year today will escalate by 3% per year. He takes the deal. a) Suppose it is December 31, 2025 now. Looking back, how much in total will he have spent on the yacht over the last 5 years? (Hint: In other words, what is the simple sum of all the amounts he has spent toward the yacht in these 5 years?) b) Realizing that he ended up spending way more than he had budgeted, he now wants to sell the yacht on December 31, 2025. The yacht can be rented out on a monthly basis starting January 2026, with the first rent accruing on Jan-31, 2026. He estimates that he can rent out the yacht at $300,000 per month, which grows at 5% per month, for a total of 60 months (after which the yacht needs to be scrapped at a salvage value of $500,000). If the rate of interest is still 18% per year, what is the price he can expect to sell the yacht for on December 31, 2025