Compound Interest

-- Section 9.1 --

 
Compound Interest: Future Value FV = PV(1 + i)kn   where 

Compound Interest: Present Value

PV = FV(1 + i)-kn    = FV (1 + i)kn  where 
 
  • FV = Future Value
  • PV = Present Value or Principal 
  • i =  r k,  r = annual rate, k = number of periods per year
  • n = number of years

Compound Interest and Annuities Click  for Calculator
 
You want to invest $20,000 for 30 years  at 11 % interest compounded quarterly.  How much money will you have at the end of the 30 years?

Solve

       Step

i = 0.11 4 = 0.0275 

k = 4, r = 0.11, Quarterly means 4 times a year

FV = PV(1 + i)kn

FV = 1,000,000, n = 30 years

FV = 20,000(1 + 0.0275)4(30)

Find the Future Value

FV = 20,000(1.0275)120 » 518,620.48

You would have $518,620.48 after 30 years. (before taxes)
Hint: don't round until you are completely finished with your calculations.

  
You want to invest $10,000 for 20 years  at 10 % interest compounded quarterly.  How much money will you have at the end of the 20 years?

[Solution]

Let's say you want to retire in 30 years with a million dollars.  You invest some money in a mutual fund that expects to earn an average of 12% per year compounded monthly.  How much money do you need to invest?

Solve

       Step

i = 0.12 12 = 0.01 

k = 12, r = 0.12, Monthly means 12 times a year
PV = FV(1 + i)-kn    = FV (1 + i)kn  Find the Present Value

PV = 1,000,000 (1 + 0.01)12(30) 

PV = 20,000, n = 30 years

PV = 1,000,000 (1 .01)360 »  27,816.69 

You would have to invest $27,816.69 to earn a million dollars after 30 years. (before taxes)
  
 Enter 1000000 (1 + 0.12 12) x (12 30) [enter or =] in your calculator
Hint: don't round until you are completely finished with your calculations.

 

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?

[Solution]

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada