(2)(30 points) Valentine's Day just happened! On 13 February people all over the world buy chocolate, and give it to the ones they love on 14 February. Then on 15 February no one even wants to look at chocolate. (a)(5 points) Assume chocolate is $10 per bag) before 14 Feb, but afterward the price drops sharply (assume $5 per bag). If you had $1000, a shrewd speculation would have been to buy 200 bags on 15 Feb 2016, and plan to sell them on 13 Feb 2018. Assuming the pre-February 14th price is the same next year as last year, what is the rate of return on your investment? NOTE I didn't say whether to assume simple or compound interest. Why doesn't it make a difference? You could get a faster Return On Investment (known as \"ROI\") if you sell the on 30 October 2017, the day before Halloween. Let's assume that the preHalloween price is $9 per bag. (b) (5 points) What t value (between 0 and 1) represents the time in years from the day after Valentine's Day to the day before Halloween? (c)(5 points) Assuming a simple interest model, what rate of return do you earn? (d)(10 points) Use the (1 + if formula and solve for i; this gives you the Internal Rate of Return (IRR). (e)(5 points) How does your answer in ((1) compare with the answers in (b) and (c)? Which would you say is the better investment? (3)(30 points) You are thinking of buying a house. You can get a loan for P : $240, 000 at annual interest rate r : 3%, with payments made monthly m : 12 for 30 years. (a)(10 points) What is your monthly payment? What is the total amount of money you pay over the time of the loan? (b)(10 points) If you can make larger payments of $1200 per month, how long will it take to pay off the loan? What is the total you pay? How much do you save? (c) (5 points) Describe the future of this loan if you make payments of only $600 per month? (d) (5 points) Describe the future of this loan if you make payments of only $500 per month