Assume that you are $30$ years old today and expect to retire when you reach age $65.$ If you were to retire today, you would like a fixed $($pretax$)$ income of $$60,000$ per year $($in addition to Social Security$)$ for a period of $15$ years $($your approximate life expectancy at age $65).$ However, you realize that price inflation will erode the purchasing power of the dollar over the next $35$ years and you want to adjust your desired retirement income at age $65$ to reflect the decline in the purchasing power of the dollar. In addition to the fixed annual income, payable at the beginning of each year starting at age $65,$ you want to have assets $($i$.$e$.,$ securities investments$)$ of $$1,000,000,$ either for your own needs or to donate to heirs, when you reach $80$ years old. Empirical studies have estimated the average compound rate of price inflation and returns on stocks and bonds over the past $70$ years to be approximately: Compound Rate Inflation $3\%$ Common stocks $11$ Corporate bonds $6$ Equally weighted portfolio $8\mathrm{.}5(50\%$ common stocks, $50\%$ bonds$)$

Assume that these rates will remain the same over the next $50$ years and that you can earn these rates of return, after transactions costs, by investing in stock and$/$or bond index mutual funds. Also assume that contributions to your retirement fund are made at the end of each year. Finally, assume that income taxes on the returns from any retirement investments $($e$.$g$.,$ IRAs or $401($k$)$ plans$)$ can be deferred until you withdraw the funds beginning at age $65.$

$1.$ Determine your required inflation$-$adjusted annual $($pretax$)$ income at age $65.$ Assume that this annual amount remains constant from age $65$ to age $80.$

$2.$ Determine the amount you must accumulate by age $65$ to meet your retirement goal, assuming that you invest in a$.$ Common stocks b$.$ Corporate bonds c$.$ Equally weighted portfolio $(50$ percent common stocks, $50$ percent bonds$)$

$3.$ Determine the annual investment in common stocks required to accumulate the funds determined in question $2,$ assuming that the first payment is made at age a$.30$ b$.40$ c$.50$

$4.$ Determine the annual investment in corporate bonds required to accumulate the funds determined in question $2,$ assuming that the first payment is made at age: a$.30$ b$.40$ c$.50$

$5.$ Determine the annual investment in an equally weighted portfolio $(50$ percent com$-$ mon stocks, $50$ percent bonds$)$ required to accumulate the funds determined in question $2,$ assuming that the first payment is made at age : a$.30$ b$.40$ c$.50$