Annuity: Present Value 
 Section 9.3  
Annuity: Payment or Rent  
Annuity: Present Value 


Compound Interest and Annuities Click for Calculator
Having just won $1,000,000 after taxes in the state lottery, how much money can you withdraw at the end of each quarter for 20 years if the banks pays 10% interest compounded quarterly. 
Solve 
Step 
i = 0.10 ÷ 4 = 0.025 
k = 4, r = 0.10, Quarterly means 4 times a year 

A is present value= 1,000,000 n = 20 years 

Find the Future Value 


You would withdraw $29,026.40 every 3 months for 20 years.  
Enter 1,000,000 × 0.025 ÷ ( 1  1.025 x^{y }( 4 × 20 ) ) ^{ } [enter or =] in your calculator  
Hint: don't round until you are completely finished with your calculations.  

Having just won $1,000,000 after taxes in the state lottery, how much money can you withdraw at the end of each month for 20 years if the banks pays 6% interest compounded monthly. 
[Solution] 


You want to deposit enough money into the bank so that you can withdraw $5,000 at the end of each month for 60 months. If the banks pays 12% interest compounded monthly, how much money should you deposit? 
Solve 
Step 
i = 0.12 ÷ 12 = 0.01 
k = 12, r = 0.12, Monthly means 12 times a year 

P is payment = 5000, n = 5 years (60 months) 
Find the Present Value  


You would have to deposit $224,775.19 so that you can withdraw $5,000 a month for 60 months.  
Enter 5,000 × ( 1  1.01 x^{y } 60 ) ^{ }÷ .01 [enter or =] in your calculator  
Hint: don't round until you are completely finished with your calculations.  

You want to deposit enough money into the bank so that you can withdraw $10,000 at the end of each month for 10 years. If the banks pays 9% interest compounded monthly, how much money should you deposit? 
[Solution] 


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Joe McDonald
Community College of Southern Nevada