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Edward deposits $250 each month into a retirement account that pays 6.00% APR (0.50% per month). What is the value of this annuity after 20 years?

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2 Answers

Since you are looking for the future value (in 20 years) of this annuity, there is a simple mathematical formula you can use to make this calculation. The formula is as follows:

        FV = PMT * [ ((1 + i)n - 1) / i ]   , where

  FV = future value

  PMT = amount of periodic payment = $250 (per month)

  i = interest rate (per month) = 0.50% / 100% = 0.005

  n = # of compounding periods = 20 years * 12 months/year = 240 (payments for 20 years)

Plug in all these given values into the above formula:

      FV = 250 * [ ((1 + 0.005)240 - 1) / 0.005 ]

           = 250 * [ (1.005240 - 1) / 0.005 ]

           = 115,510.22379037

           ≈ 115,510.22

Thus, the value of this annuity after 20 years is approximately $115,510.22

Academic honesty.  I looked this formula up from text.  It is too easy to make an error deriving it and I felt lazy.

 

P  =  A((1 + (i/q))^(n/q)   -  1)(q/i)

where P is the principal after years

A is the amount deposited each interval (month)

i = interest rate (.06)

q = no. of pay periods/ year (12)

n = no of years. 20

= 115,510.22.  Almost double the amount paid in (60000)