if $1200 are deposited into an account with a 11% interest rate, compounded monthly, what is the balance…

if $1200 are deposited into an account with a 11% interest rate, compounded monthly, what is the balance after 11 years? f = $? f = p(1 + \\frac{r}{n})^{nt} round to the nearest cent.

if $1200 are deposited into an account with a 11% interest rate, compounded monthly, what is the balance after 11 years? f = $? f = p(1 + \\frac{r}{n})^{nt} round to the nearest cent.

Answer

Explanation:

Step1: Identify the values

$P = 1200$, $r=0.11$, $n = 12$ (monthly compounding), $t = 11$

Step2: Substitute into the formula

$F=1200\times(1+\frac{0.11}{12})^{12\times11}$ First, calculate the value inside the parentheses: $\frac{0.11}{12}\approx0.009167$, then $1+\frac{0.11}{12}=1 + 0.009167=1.009167$. Next, calculate the exponent: $12\times11 = 132$. So $F = 1200\times(1.009167)^{132}$.

Step3: Calculate $(1.009167)^{132}$

Using a calculator, $(1.009167)^{132}\approx3.49777$.

Step4: Calculate $F$

$F=1200\times3.49777 = 4197.324$. Rounding to the nearest cent, $F\approx4197.32$.

Answer:

$4197.32$