Question

4. Determine which investment is best. Evan plans to invest $10000 for 8 years. a. Better Banks offers an 8 year CD at an annual rate of 5% using simple interest. b. America's Bank offers an 8 year CD at annual rate of 4.7% using monthly compound interest. c. Union Bank offers an 8 year CD at an annual rate of 4.5% using continuous compounding.

Answer 1

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:

$A(t) = A(0)(1 + rt)$

In which:

• A(0) is the initial amount.

• r is the interest rate, as a decimal.

The compound interest formula 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.

The formula for continuous compounding is given by:

$A(t) = Pe^{kt}$

Hence, applying the formulas, for each item, we will find the total amount.

Item a:

$A(t) = A(0)(1 + rt)$

$A(t) = 10000[1 + 0.05(8)]$

$A(t) = 14000$

Item b:

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

$A(t) = 10000\left(1 + \frac{0.047}{12}\right)^{12(8)}$

$A(t) = 14554$

Item c:

$A(t) = Pe^{kt}$

$A(t) = 10000e^{0.045(8)}$

$A(t) = 14333$

Due to the highest amount, option b is the best.

More can be learned about interests at https://brainly.com/question/25781328