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.)
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:
$28154.05$