if $360 is invested at an interest rate of 4%...
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:
$x=-6$