Respuesta :
The investment with the biggest total amount, considering the interests, is given by:
b. America's Bank offers an 8 year CD at annual rate of 4.7% using monthly compound interest.
Interest formulas
The simple interest formula is given by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
- A(0) is the initial amount.
- r is the interest rate, as a decimal.
The compound interest formula 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.
The formula for continuous compounding is given by:
[tex]A(t) = Pe^{kt}[/tex]
Hence, applying the formulas, for each item, we will find the total amount.
Item a:
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]A(t) = 10000[1 + 0.05(8)][/tex]
[tex]A(t) = 14000[/tex]
Item b:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(t) = 10000\left(1 + \frac{0.047}{12}\right)^{12(8)}[/tex]
[tex]A(t) = 14554[/tex]
Item c:
[tex]A(t) = Pe^{kt}[/tex]
[tex]A(t) = 10000e^{0.045(8)}[/tex]
[tex]A(t) = 14333[/tex]
Due to the highest amount, option b is the best.
More can be learned about interests at https://brainly.com/question/25781328
