10. Suppose today is Dec 31st, 2020, and as always, today is time t=0. Prithu wants...

 

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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? 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?