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New Milford, CT

Hi Kelli!

Ok this problem involves something called the Annuity Due Payment, and there is a standard formula for solving this type of problem:

Pmt=PV * ( r / ( 1-(1+r)^{-n} ) ) * 1/(1+r)

where Pmt is the annual payment ($6,000.00 in this case), PV is the present value, or the amount deposited today, r is the interest rate per period (6%), and n is the number of periods (10). So, we have to plug a few things in:

$6,000 = PV * ( 0.06 / (1-1.06^{-10}) ) * 1/1.06

Multiplying out the right hand side gives us

$6,000 = PV * 0.128177319

Dividing both sides by 0.128177319 yields

To illustrate what happens to this money, I will write a quick table for you:

1 46,810.15 40,810.15

2 43,258.76 37,258.76

3 39,494.28 33,494.28

4 35,503.94 29,503.94

5 31,274.18 25,274.18

6 26,790.63 20,790.63

7 22,038.07 16,038.07

8 17,000.35 11,000.35

9 11,660.37 5,660.37

10 5,999.99 0.00

3 39,494.28 33,494.28

4 35,503.94 29,503.94

5 31,274.18 25,274.18

6 26,790.63 20,790.63

7 22,038.07 16,038.07

8 17,000.35 11,000.35

9 11,660.37 5,660.37

10 5,999.99 0.00

In the table above, for n = 2 and greater, PV was calculated by adding interest of 1.06X from the remaining balance from the previous period after the withdraw of $6,000.00 was made.

John M.

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Yang X.

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