8 fill in the blank 1 point brendan borrows $4200 with a 2.2% annual interest rate compounded monthly. if…

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 form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P = 4200$, $r=0.022$ (since $2.2%=0.022$), $n = 12$ (compounded monthly).

Step2: Calculate amount after 2 years

Substitute $t = 2$ into the formula: $A=4200(1 +\frac{0.022}{12})^{12\times2}$ $A=4200(1+\frac{0.022}{12})^{24}$ First, calculate $1+\frac{0.022}{12}\approx1 + 0.001833=1.001833$. Then, $(1.001833)^{24}\approx1.047767$. So, $A = 4200\times1.047767\approx4400.62$.

Step3: Calculate amount after 3 years

Substitute $t = 3$ into the formula: $A=4200(1+\frac{0.022}{12})^{12\times3}$ $A=4200(1+\frac{0.022}{12})^{36}$ $(1+\frac{0.022}{12})\approx1.001833$. $(1.001833)^{36}\approx1.075529$. So, $A = 4200\times1.075529\approx4517.22$.

Answer:

After 2 years: $$4400.62$ After 3 years: $$4517.22$