Question

1. You are 21 years old and are concerned about your retirement. You want to live comfortably when you retire 49 years from now. Since you won’t have a house payment (you expect to have the mortgage paid off by then), you figure you will need only $4,000 a month (current dollars) on which to live. You expect inflation to remain at 2.25% for the 49-year period, and you expect $1,850 (current dollars) in social security when you retire at 70 years of age. You expect to live 20 years in retirement. How much do you need to save every month, assuming a 6% annual return on your savings, beginning now?

Answer 1

Expected monthly expenses from yr 70 to yr 90=$4000 per month (on current dollars)

Expected monthly expenses form yr 70 to yr 90 in $ terms as at yr 70=Future value of 4000 at inflation rate of 2.25% for 49 years=11,900.43

Present value of monthly expenses from yr 70 to yr 90 in $ terms as at yr 70=Present value of 11,900.43 for 20 yrs at 6%=1,36,496.95

Expected value of social security in $ terms as at yr 70=Future value of 1850 at 6% rate for 49 years=32148.38

Hence, expected value of savings must grow to (136,496.95-32148.38=104348.57)

Savings required per month=PMT calculated with investment rate of 6% for 49 years and future value of 104348.57

=382.29