You are thirty$-$five years old with a steady job and no debt. Your financial capital is worth $$150,000$ and is

invested entirely in the stock market in mutual funds. Your current salary is $$50,000$ per year $($payable at the

end of the year$),$ and is expected to grow by $5\%$ per year until you retire at age sixty$-$two. You expect to live

until you are eighty years old. Assume that the minimum level of expenses that you need is $$18,000$ per year,

and that this amount is growing at the rate of $2\%$ per year.

$(1)$ What is the value of your current economic net worth, assuming an interest rate of $6\%$ p$.$a$.,$ annual

compounding?

$(2)$ Now imagine that $($overnight$)$ the stock market crashes and your financial capital falls by $40\%.$ However, at

the same time interest rates have dropped by $200$ basis points so the "new" interest rate is $4\%$ p$.$a$.,$ annual

compounding. What is the revised value of your economic net worth? Why has it declined$/$increased$?$