Question 1093808: Please help with this problem:How much money would you need to deposit today at 5% annual interest compounded monthly to have $20000 in the account after 9 years?
Thanks!
Found 2 solutions by MathTherapy, greenestamps:
Answer by MathTherapy(10555)   (Show Source):
You can put this solution on YOUR website!
Please help with this problem:How much money would you need to deposit today at 5% annual interest compounded monthly to have $20000 in the account after 9 years?
Thanks!
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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