Question

The balance in Meg's savings account can be calculated using the
formula S = 50(1.0304), where y is the number of years from the initial
deposit. Meg switches to an account that compounds interest each
month. Which account has about the same annual interest rate as Meg's
current savings account if mis the number of months from the initial
deposit?
S = 50(1.0002)
(B
S = 50 (1.0025)
S = 50(1.0859)
D S = 50(1.2331)

Answer 1

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:

$S = 50(1.0025)^y$

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

$A(t) = P\left(1 + \frac{r}{n}\right)^{nt}$

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:

$S(y) = 50(1.0304)^y$

Hence r = 0.0304.

Considering monthly interest, we have that:

$r_m = \frac{0.0304}{12} = 0.0025$

Hence, the desired account has the equation given by:

$S = 50(1.0025)^y$

You can learn more about compound interest at https://brainly.com/question/25781328