Use the present value formula for $1: , with:

 = Present Value, or Principal invested, or INITIAL amount deposited (Unknown, in this case)

 = Accumulated amount, or future value ($20,000, in this case)

 = Annual Interest rate (5%, or .05, in this case)

 = Number of ANNUAL compounding periods (monthly, or 12, in this case)

 = Time, in years (9, in this case)



 becomes: , and then Present Value, or  

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!
 
Ooh! A present value formula for working a problem involving compound interest.  Certainly valid; but not easy to understand, so not the way I would go.


You are starting with some unknown amount x.

The money is accruing interest monthly for 9 years; that is 9*12 =108 months.

The annual interest rate is 5%, or .05; the periodic (monthly) interest rate is one-twelfth of that, let's just call it (.05/12).

The "growth factor" -- what the value of the account gets multiplied by each time interest is gained, is 1 plus the periodic interest rate; in this case (1+.05/12).

The growth factor is applied to the beginning amount 108 times (monthly for 9 years).


So, since we want the value after the 9 years to be $20,000,





 

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