attached
1. Sam Hill has just won the state lottery, paying $200,000 yearly for the next 30 years. Sam will receive his first payment today. If the interest rate is 5%, what is the present value of his lottery winnings? (Enter a positive value and round to 2 decimals) 2. The United Kingdom has a consol bond that pays a $100 coupon every 6 months (semi-annually), forever. If the next payment is due exactly six months from today and the discount rate is 7% APR (compounded semi-annually), then calculate the present value of this investment. (Enter a positive value and round to 2 decimals) 3. Suppose you put $3,500 per month into a Roth IRA starting one month from today, that pays 9% APR (compounded monthly). Assume you have nothing saved today. Calculate the future value of the retirement account 23 years from today. (Enter a positive value and round to 2 decimals) 4. April Stigum will receive a 20-year annuity of $8,000 annually, beginning five years from today. In other words, the first payment will be made at the end of year 5. Assuming a required rate of return of 10%, calculate the present value today of her annuity. (Enter a positive value and round to 2 decimals) 5. Joe and Sarah Fabozzi are saving for the college education of their newborn daughter (born today), Beth. The Fabozzi's estimate that college expenses will run $30,000 per year when their daughter reaches college in 18 years. In other words, the first withdrawal will be made on Beth's 18th Birthday, and the last payment will be made on Beth's 17th Birthday. The expected interest rate while saving and in college is 6%. The first deposit will be made one year from today. Calculate the annual payment the Fabozzi's must make to the account so that their daughter will be completely supported through four years of college. (Enter a positive value and round to 2 decimals) 6. George Anders has just been offered a job at $85,000 per year, with the first payment made one year from today. He anticipates his salary will grow by 2% per year until his retirement in 25 years. Given an interest rate of 6%, calculate the present value of his lifetime salary. (Enter a positive value and round to 2 decimals) 7. You are looking at buying a home with an asking price of $975,000. Since the market is hot, you plan to put in an offer for the full asking price. You also plan to put $195,000 down and finance the remainder. Your bank offers you a 30-year loan at 4.5% APR (compounded monthly). Assume your first payment is made one month from today. Calculate your monthly loan payment. (Enter a positive value and round to 2 decimals) 8. You have 30 years left until retirement, and you want to retire with $5,000,000 saved. You plan to deposit 1,800 dollars into the account each month beginning one month from today. You currently have $400,000 saved. Calculate the rate of return (APR) you need to earn to reach your retirement goal. (Enter percentages as decimals and round to 4 decimals) 9. Tom Tom Co. has been working on new technology. This new technology will be available in the near term, and the firm's CEO anticipates the first cash flow to be $1,000,000, received 10 years from today. Subsequent annual cash flows will grow at 5% in perpetuity. Calculate the value of the technology today if the discount rate is 12%? 10. You just won the Power Ball Lottery worth $134,000,000. Upon reading the fine print, you learn that you have two options: Option A: take the cash value of $75.3 million today (before taxes) Option B: The winner is guaranteed to receive 30 graduated payments over 29 years; the first payment is made today. These payments will increase by 3% per year until the final payment. The first payment, received today, equals $6,000,000. Assuming a required rate of return of 5%, calculate the present value of option B. 11. Your friend is celebrating her birthday and wants to start saving for retirement. She has provided you with the following information: Years until retirement: 25 Amount to withdraw each year in retirement: $110,000 Years to withdraw in retirement: 15 Interest rate while saving: 9% Interest rate in retirement: 6% Saved today: $100,000 The first deposit will be made one year from today, and the last deposit will be made on the day she retires. Her first withdrawal will not occur until one year after she retires, and she plans to spend her entire nest egg. Calculate the amount she will need to have saved on the day she retires. (Enter a positive value and round to 2 decimals) 12. Your friend is celebrating her birthday and wants to start saving for retirement. She has provided you with the following information: Years until retirement: 25 Amount to withdraw each year in retirement: $110,000 Years to withdraw in retirement: 15 Interest rate while saving: 9% Interest rate in retirement: 6% Saved today: $100,000 The first deposit will be made one year from today, and the last deposit will be made on the day she retires. Her first withdrawal will not occur until one year after she retires, and she plans to spend her entire nest egg. Calculate the amount she will need to deposit each year to reach her retirement goal. (Enter a positive value and round to 2 decimals) 13. Your friend is celebrating her birthday and wants to start saving for retirement. She has provided you with the following information: Years until retirement: 25 Amount to withdraw each year in retirement: $110,000 Years to withdraw in retirement: 15 Interest rate while saving: 9% Interest rate in retirement: 6% Saved today: $100,000 The first deposit will be made one year from today, and the last deposit will be made on the day she retires. Her first withdrawal will not occur until one year after she retires, and she plans to spend her entire nest egg. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump-sum deposit today to cover her retirement needs. She plans to spend what she has currently saved today on a new car. Calculate the amount she will need to deposit today to reach her retirement goal. (Enter a positive value and round to 2 decimals)