$25,000 are deposited into an account with a 3.45% interest rate, compounded semi - annually (2 times per…

$25,000 are deposited into an account with a 3.45% interest rate, compounded semi - annually (2 times per year). find the accumulated amount after 25 years. hint: a = p(1 + \\frac{r}{k})^{kt} round your answer to the nearest cent (hundredth).

$25,000 are deposited into an account with a 3.45% interest rate, compounded semi - annually (2 times per year). find the accumulated amount after 25 years. hint: a = p(1 + \\frac{r}{k})^{kt} round your answer to the nearest cent (hundredth).

Answer

Explanation:

Step1: Identify the values of P, r, k, and t

$P = 25000$, $r=0.0345$, $k = 2$, $t = 25$

Step2: Substitute the values into the compound - interest formula

$A=25000\left(1+\frac{0.0345}{2}\right)^{2\times25}$

Step3: Calculate the value inside the parentheses

$1+\frac{0.0345}{2}=1 + 0.01725=1.01725$

Step4: Calculate the exponent

$2\times25 = 50$

Step5: Calculate the power

$(1.01725)^{50}\approx2.33797$

Step6: Calculate the accumulated amount A

$A = 25000\times2.33797=58449.25$

Answer:

$58449.25$