question 2\nthis question has two parts. first, answer part a. then, answer part b.\npart a\nfinance corey…

Explanation:

Step1: Recall 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 interest is compounded per year, and $t$ is the number of years. Given $P = 2100$, $r=0.042$ (since $4.2%=0.042$), and $n = 12$ (compounded monthly). The function for the balance $A$ in the account after $t$ years is $A(t)=2100(1 +\frac{0.042}{12})^{12t}=2100(1 + 0.0035)^{12t}=2100(1.0035)^{12t}$.

Step2: Calculate balance after 5 years

Substitute $t = 5$ into the function $A(t)$. $A(5)=2100(1.0035)^{12\times5}=2100(1.0035)^{60}$. $(1.0035)^{60}\approx1.232997$. $A(5)=2100\times1.232997\approx2589.29$.

Step3: Calculate balance after 10 years

Substitute $t = 10$ into the function $A(t)$. $A(10)=2100(1.0035)^{12\times10}=2100(1.0035)^{120}$. $(1.0035)^{120}\approx1.521997$. $A(10)=2100\times1.521997\approx3196.19$.

Answer:

Part A: $A(t)=2100(1.0035)^{12t}$ Part B: b. $$2589.29$ c. $$3196.19$