Question

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.

Answer 1

The simplified answer is y = 1000(1.03)x.

Answer 2

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.