Answer :
Answer:
[tex]A(t) = 1000(1.0025)^{12t}[/tex]
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money in the account after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the number of years the money is invested or borrowed for.
For this problem, we have that:
[tex]P = 1000[/tex]
The investment is compounded monthly. There are 12 months in a year. So [tex]n = 12[/tex]
The interest rate is 3%. So [tex]r = 0.03[/tex].
So
The amount of money in her account after t years is:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 1000(1 + \frac{0.03}{12})^{12t}[/tex]
[tex]A(t) = 1000(1.0025)^{12t}[/tex]