Eloise is investing in a retirement account. she plans on adding an additional $50 at the end of every year and the expected monthly rate of return is 3% of the amount invested, calculated at the end of the month. if she starts with $1000 in the account find an equation that models the amount of money in the account each month for the first year.

The accumulated (future) value is given by the formula
F=P(1+i)^n
where 
P=amount of deposit (made at the beginning of the first period)
i=monthly interest, APR/12 = 3%/12 =0.0025
n=number of periods (month)

For example, the future value for the 6th month is
F(6)=1000(1.0025^6)=1015.09  (to the nearest cent)

Here is a schedule of the values,
i=month
F(i) = value at the end of month i.

  i   F(i)
 0  1000.0 
 1  1002.5 
 2  1005.01
 3  1007.52
 4  1010.04
 5  1012.56
 6  1015.09
 7  1017.63
 8  1020.18
 9  1022.73
10 1025.28
11 1027.85
12 1030.42 + $50 deposit = 1050.42
All values are rounded to the nearest cent.

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