Solution for Problem 9.1.2

Let's say you want to retire in 20 years with a million dollars.  You invest some money in a mutual fund that expects to earn an average of 8% per year compounded monthly.  How much money do you need to invest?

Solve

       Step

***   i = 0.08 12 » 0.006

k = 12, r = 0.08, Monthly means 12 times a year
PV = FV(1 + i)-kn    = FV (1 + i)kn  Find the Present Value

PV = 1,000,000 (1 + 0.006)12(30) 

FV = 1,000,000, n = 20 years

PV = 1,000,000 (1 .006)360 »  91,443.37 

You would have to invest $91,443.37 to earn a million dollars after 20 years.. (before taxes)
  
*** Don't round.  Enter 1000000 (1 + 0.08 12) x (12 30) [enter or =] in your calculator
Hint: don't round until you are completely finished with your calculations.