1. You can deposit $10,000 into an account paying 9% annual interest either today or exactly 10 years from today. How much better off will you be at the end of 40 years if you decide to make the initial deposit today rather than 10 years from today? 2. You want to borrow $600,000 to buy an apartment, and you can only afford $4,000 a month to repay the loan. Suppose the bank charges you a fixed interest rate of 4% with monthly compounding. How long will it take you to pay off the loan? 3. Assume that you just won the state lottery. Your prize can be taken either in the form of $40.000 at the end of each of the next 25 years (that is, $1,000,000 over 25 years) or as a single amount of $500,000 paid immediately. a. If you expect to be able to earn 5% annually on your investments over the next 25 years, ignoring taxes and other considerations, which alternative should you take? Why? b. Would your decision in part a change if you could earn 7% rather than 5% on your investments over the next 25 years? Why?