Respuesta :
Using compound interest, it is found that the account that has about the same annual interest rate as Meg's current savings account is given by:
[tex]S = 50(1.0025)^y[/tex]
What is compound interest?
The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
- A(t) is the amount of money 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 year.
- t is the time in years for which the money is invested or borrowed.
In this problem, considering yearly interest, we have that the equation is:
[tex]S(y) = 50(1.0304)^y[/tex]
Hence r = 0.0304.
Considering monthly interest, we have that:
[tex]r_m = \frac{0.0304}{12} = 0.0025[/tex]
Hence, the desired account has the equation given by:
[tex]S = 50(1.0025)^y[/tex]
You can learn more about compound interest at https://brainly.com/question/25781328
