The Smiths are planning to retire in 35 years. They want an annual real income of $45,000, paid at the end of each month of their expected 20-year retirement and to bequeath $500,000, in real dollars, to their son at the end of their retirement. In addition, their son’s 4-year university education, to begin in 8 years, is expected to cost $ 10,000 real dollars per year, due at the start of each year. They recently purchased a house for $250,000, with $50,000 cash and a $200,000, 20-year mortgage, carrying a 7% interest rate, compounded monthly and paid monthly. Over the next 55 years, the nominal house value is expected to grow 4% annually. The Smiths plan to live in their house for the rest of their lives, and the house will be sold on their demise. The expected annual inflation rate is 3%. The Smiths expect to earn 6% nominal effective annual interest rate on their retirement savings.
a. How much do they need to save in real dollars at the end of each month, for the next 35 years, on top of their monthly mortgage payment, to meet their financial goals? Clearly state any assumptions you make.
b. What will be the total real and nominal mortgage payment plus savings in the last month of the mortgage?
c. How much do they need to save in real and nominal terms in the last month before retirement?