Respuesta :
Answer:
Money in Megan saving accounts is $2758.74
Step-by-step explanation:
Formula for compound interest is given as,
[tex]A=P\left(1+i\right)^{n}[/tex]
where, m : number of compounding periods per year
i : rate per compounding period = r/ m
n : total no. of compounding periods = m * no. of years.
P : principal ( present value)
A : amount ( future value ) at the end of n periods
Now calculate the value of above terms.
Since it is given that interest is compounded semi annually.
Therefore value of m is m = 2.
Given that rate is 2% that is, r = 0.02
Also number of years is 7 that is, t = 7
Therefore formula becomes,
[tex]A=P\left(1+\dfrac{r}{m}\right)^{m \times t}[/tex]
Substituting the values in the formula,
[tex]A=2400\left(1+\dfrac{0.02}{2}\right)^{2 \times 7}[/tex]
Simplifying,
[tex]A=2400\left(1+0.01\right)^{14}[/tex]
[tex]A=2400\left(1.01\right)^{14}[/tex]
[tex]A=2400 \times 1.149474213[/tex]
[tex]A=2758.738111[/tex]
Rounding to two decimal places, A = $ 2758.74
Therefore, Megan has total of $ 2758.74 in her saving account.
