Respuesta :
Using compound interest, it is found that you will have $3,182.7.
Compound interest:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
- 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:
- Compounded semiannually, hence [tex]n = 2[/tex].
- 6% interest, hence [tex]r = 0.06[/tex].
- Deposit of $3,000, hence [tex]P = 3000[/tex].
- End of one year, hence [tex]t = 1[/tex].
Then:
[tex]A(1) = 3000\left(1 + \frac{0.06}{2}\right)^{2} = 3182.7[/tex]
You will have $3,182.7.
To learn more about compound interest, you can take a look at https://brainly.com/question/25781328
