a) Emma won a $10,000,000 state lottery. She has two (2) options. Option 1 allows her to claim her money as 20 year payments of $2,000,000 each, and option 2 allows her to take $10,000,000 today. If the interest rate is 3%, which option should she take?
b) Jack is 30 years old and has decided to start saving for retirement. To achieve his financial goals, he plans to save $12,000 annually at the end of each year until he reaches age 65. If the account earns 4% per year, how much will he have in the account at age 65?
c) Victoria is 35 years old and has decided to start saving for retirement. To achieve his financial goals, she plans to save $12,000 annually at the end of the first year, and expects to her savings to increase by 10% per year thereafter. If the account earns 6% per year, how much will she have in the account at age 65?
d) Find the present value and future value of an investment that pays 8% annually and makes the following end-of-year payments.
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
$1,000 $2,000 $4,000 $6,000 $9,000
e) Jane wants to endow an annual exhibition at the art gallery of her alma mater. She allocates $20,000 per year forever to this event. If the university earns 12% per year on its investments, and if the event is in one year’s time, how much will she need to donate to endow the exhibition?