watch the video and then solve the problem given below. click here to watch the video. use the compound…

watch the video and then solve the problem given below. click here to watch the video. use the compound interest formulas a = p(1 + r/n)^(nt) and a = pe^(rt) to solve the problem given. round answers to the nearest cent. find the accumulated value of an investment of $25,000 for 3 years at an interest rate of 4% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously. a. what is the accumulated value if the money is compounded semiannually? $ (round your answer to the nearest cent.)

watch the video and then solve the problem given below. click here to watch the video. use the compound interest formulas a = p(1 + r/n)^(nt) and a = pe^(rt) to solve the problem given. round answers to the nearest cent. find the accumulated value of an investment of $25,000 for 3 years at an interest rate of 4% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously. a. what is the accumulated value if the money is compounded semiannually? $ (round your answer to the nearest cent.)

Answer

Explanation:

Step1: Identify the values

$P = 25000$, $r=0.04$, $t = 3$. For semi - annual compounding, $n = 2$.

Step2: Substitute into compound - interest formula

Use $A=P(1 +\frac{r}{n})^{nt}$. Substitute the values: $A = 25000(1+\frac{0.04}{2})^{2\times3}$.

Step3: Simplify the exponent and fraction

First, $\frac{0.04}{2}=0.02$ and $2\times3 = 6$. So $A = 25000(1 + 0.02)^{6}$.

Step4: Calculate $(1 + 0.02)^{6}$

$(1 + 0.02)^{6}=1.02^{6}\approx1.126162$.

Step5: Calculate the accumulated value

$A=25000\times1.126162 = 28154.05$.

Answer:

$28154.05$