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 + \\frac{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? $28154.06 (round your answer to the nearest cent.) b.what is the accumulated value if the money is compounded quarterly? $28,170.63 (round your answer to the nearest cent.) c. what is the accumulated value if the money is compounded monthly? $ (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 + \\frac{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? $28154.06 (round your answer to the nearest cent.) b.what is the accumulated value if the money is compounded quarterly? $28,170.63 (round your answer to the nearest cent.) c. what is the accumulated value if the money is compounded monthly? $ (round your answer to the nearest cent.)

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times compounded per year, and $t$ is the number of years. Given $P=$25000$, $r = 0.04$, $t = 3$ years. For monthly compounding, $n = 12$.

Step2: Substitute the values into the formula

$A=25000(1 +\frac{0.04}{12})^{12\times3}$ First, calculate the value inside the parentheses: $\frac{0.04}{12}\approx0.003333$, then $1+\frac{0.04}{12}=1.003333$. And $12\times3 = 36$. So $A = 25000\times(1.003333)^{36}$.

Step3: Calculate $(1.003333)^{36}$

Using a calculator, $(1.003333)^{36}\approx1.127271$.

Step4: Calculate the value of $A$

$A=25000\times1.127271=$28181.78$

Answer:

$28181.78$