question 1 how much will be accumulated in an account with an initial deposit of $100, and which earns 10%…

Explanation:

Step1: Identify 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), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Given $P=$100$, $r = 0.10$ (since 10%=0.10), $n = 4$ (compounded quarterly), and $t = 3$.

Step2: Substitute values into the formula

$A=100(1 +\frac{0.10}{4})^{4\times3}=100(1 + 0.025)^{12}$. First, calculate $1+0.025=1.025$. Then, find $(1.025)^{12}$. Using a calculator, $(1.025)^{12}\approx1.344888824$.

Step3: Calculate the final amount

$A = 100\times1.344888824=$134.49$ (rounded to the nearest cent).

Answer:

C. $134.49$