You have just had your 30th birthday. You have two children, one of which will g

Question

You have just had your 30th birthday. You have two children, one of which will go to college 10 years from now and require four beginning-of-the-year payments for college expenses of $10,000, $11,000, $12,000, and $13,000. Your second child will go to college 15 years from now and require four beginning-of-the-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.

What equal, annual, and end-of-the-year amount must you save for each of the next 30 years to meet these goals, if all savings earn a 13% annual rate of return?

Explanation / Answer

The payoff from the put option is $0 if the stock price rises and $9 if the stock price falls. From the binomial pricing model we can create a replicating portfolio with the following two equations:

$0 = ($23.50 × x) + (1.03 × y)

$9 = ($9 × x) + (1.03 × y)

x = –0.62 shares of stock

y = $14.16 of risk-free bonds

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