The bank offers special savings accounts that give continuously compounding interest with interest rates corresponding to different plans. (a) You want the value looking ahead 5 years of your account to be 100,000 dollars, but you only have 80,000 dollars today. What interest rate do you need the bank to offer to accomplish this? Answer: (b) You decide to take the mattress investment plan which offers a devastating 0% interest. If you contribute to your account at a constant 5000 dollars per year, then what is the accumulated future value of your account after 10 years. Answer: (c) Your friend decides to take the "better investment plan which offers 10% interest. If they contribute to their account at a non-constant rate of 2000e to dollars per year, then what is the accumulated future value of their account after 10 years. Answer: (d) Your brother decides to also use the "better" investment plan which offers 10% interest. He contribute a one time deposit of 20,000 dollars. What is the future value of his account after 10 years? Answer: (e) Your mother decides on the "best" investment plan which offers 25% interest. She contributes a non-constant 3000 dollars per year. What is the accumulated present value of her account after 10 years