Annuity:  Present Value

-- Section 9.3 --

 
Annuity: Payment or Rent

Annuity: Present Value

 
  • PV = Present Value
  • P = Payment or Rent 
  • A = Future Value
  • i =  r k,  r = is annual rate, k = number of periods per year
  • n = number of years

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 xy ( -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 xy - 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