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 

Compound Interest and Annuities
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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^{y } (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