1. As a result of winning the Gates Energy Innovation Award, you are awarded a growing perpetuity. The first payment will occur in a year and will be for $20,000. You will continue receiving monetary awards annually with each award increasing by 5% over the previous award, and these monetary awards will continue forever. If the appropriate interest rate is 10%, what is the present value of this award?
2. What is the future value of each of the following streams of payments?a. $500 a year for 10 years compounded annually at 5 percent?
3. What is the present value of the following annuities?a. $2,500 a year for 10 years discounted back to the present at 7 percent?
4. Carol Calc plans on retiring on her 60th birthday. She wants to put the same amount of funds aside each year for the next twenty years -- starting next year -- so that she will be able to withdraw $50,000 per year for twenty years once she retires, with the first withdrawal on her 61st birthday. Carol is 20 years old today. How much must she set aside each year for her retirement if she can earn 10% on her funds?