Answer Happy

You have just had your 30th birthday. You have two children. One
will go to college 10 years from now and require four
beginning-of-year payments for college expenses of $10,000,
$11,000, $12,000 and $13,000. The second child will go to college
15 years from now and require four beginning-of-year payments for
college expenses of $15,000, $16,000, $17,000 and $18,000. In
addition, you plan to retire in 30 years. You want to be able to
withdraw $50,000 per year (at the end of each year) from an account
throughout your retirement. You expect to live 20 years beyond
retirement. The first withdrawal will occur on your 61st birthday.
In addition to that, you are planning for buying a cabin in the
mountains 8 years from now at an estimated cost of $80,000. You can
afford to save only $2,000 per year at the end of each year for the
first 12 years.
Required:
What equal, annual, end-of-year amount must you save for year 13
to 30 to meet these goals, if all savings earn a 13 per cent annual
rate of return?