# Grace deposits $1000 in a mutual fund earning 9.5% annual interest, compounded monthly.write an exponential function that models this situation where y is the amount of grace's investment and x is...

Grace deposits $1000 in a mutual fund earning 9.5% annual interest, compounded monthly.

write an exponential function that models this situation where y is the amount of grace's investment and x is time in years. use your equation to complete the chart round to the nearest cent. use your data to graph x-scale of 5 years and a y-scale of $1000.) if grace were to invest $1000 at age 25 and not withdraw any money until retirement at age 67, calculate the expected value of her investment. show your calulations and consider the trend of your graph.

YEARS BALANCE

5

10

15

20

25

30

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Since the investment is compounded every month, the amount that it increases by is `(1+0.095/12)` , which means that after n months, the amount in the account is

`A=1000(1+0.095/12)^n` and after t years, the amount is:

`A=1000(1+0.095/12)^{12t}`

This means that we get for each value of the chart:

t=5, A=$1605.01

t=10, A=$2576.06

t=15, A=$4134.59

t=20, A=$6636.06

t=25, A=$10650.94

t=30, A=$17094.86

**Also, if she retires at 67, then there are 67-25=42 years of investment, which gives A=$53212.28. The graph of this function is:**

actually its

5-1603.42

10-2570.95

15-4122.31

20-6609.78

25-10598.24

30-16993.40

and the formula is 1000(1.0079)12x