14) A local bank is running the following advertisement in the newspaper: For just $1000 we will pay you $100 forever! The fine print in the ad says that for a $1000 deposit, the bank will pay $100 every year in perpetuity, starting one year after the deposit is made.

a) What interest rate is the bank advertising (what is the rate of return of this investment)?

b) What is the interest rate if the first payments started two years after the deposit is made?

15) You have just turned 22 years old, have just received your bachelors degree, and have accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earns 7% per year. You cannot make withdrawals until you retire on your sixty-fifth birthday. After that point, you can make withdrawals as you see fit. You believe that you will live to 100 and work until you turn 65. You estimate that to live comfortably in retirement, you will need $100,000 per year, starting at the end of the first year of retirement and ending on your one hundredth birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your retirement?