if $360 is invested at an interest rate of 4% per year and is compounded quarterly, how much will the…

if $360 is invested at an interest rate of 4% per year and is compounded quarterly, how much will the investment be worth in 18 years? use the compound interest formula $a = p(1+\frac{r}{n})^{nt}$. \n$175.86\n$422.39\n$430.61\n$736.96\nquestion 9(multiple choice worth 1 points)\n(05.01 mc)\nsolve $\frac{1}{25}=5^{x + 4}$\n$x=-\frac{7}{2}$\n$x = - 6$\n$x=\frac{9}{2}$

if $360 is invested at an interest rate of 4% per year and is compounded quarterly, how much will the investment be worth in 18 years? use the compound interest formula $a = p(1+\frac{r}{n})^{nt}$. \n$175.86\n$422.39\n$430.61\n$736.96\nquestion 9(multiple choice worth 1 points)\n(05.01 mc)\nsolve $\frac{1}{25}=5^{x + 4}$\n$x=-\frac{7}{2}$\n$x = - 6$\n$x=\frac{9}{2}$

Answer

Question 1

Explanation:

Step1: Identify values for formula

$P = 360$, $r=0.04$, $n = 4$, $t = 18$.

Step2: Substitute into compound - interest formula

$A=P(1 +\frac{r}{n})^{nt}=360(1+\frac{0.04}{4})^{4\times18}$.

Step3: Calculate inside the parentheses first

$1+\frac{0.04}{4}=1 + 0.01=1.01$.

Step4: Calculate the exponent

$4\times18 = 72$.

Step5: Calculate the power

$1.01^{72}\approx2.04711$.

Step6: Multiply by $P$

$A = 360\times2.04711\approx736.96$.

Answer:

$736.96$

Question 2

Explanation:

Step1: Rewrite $\frac{1}{25}$ as a power of 5

$\frac{1}{25}=5^{- 2}$, so the equation becomes $5^{-2}=5^{x + 4}$.

Step2: Set exponents equal

Since the bases are the same, we have $-2=x + 4$.

Step3: Solve for $x$

$x=-2 - 4=-6$.

Answer:

$x=-6$