Alex and Amy are both 29 years old and intend to retire when they are 67. They expect to live 20 years after their retirement, and would like to spend $5,000 per month in today’s dollars at retirement. Assume inflation is 4.00 percent and that they can invest at 7.50 percent per year, compounded annually. They have already saved $19,000 towards their retirement goal. How much do they need to save at the end of each month in order to achieve their goal of having enough money for retirement? Assume that Alex and Amy do not intend to make additional savings toward this goal after retirement, but will continue to invest their current savings

What is the future value of $19,000 by the time of Alex and Amy’s retirement? $ until the end of their retirement life.

1. What is the real rate of return?  %      

2. What amount should Alex and Amy have saved (including returns on investment) by the time of their retirement? Said differently, what is the present value of their retirement needs at age 67?   

3. What is the future value of $19,000 by the time of Alex and Amy’s retirement? $

4, If Alex and Amy made no further savings contributions over the next 38 years, what would be the size of the savings deficit (the difference between retirement needs and current savings) when they are 67?