if $550 are deposited into an account with 9% interest rate, compounded monthly, what is the balance after 6…

if $550 are deposited into an account with 9% interest rate, compounded monthly, what is the balance after 6 years? solve for f, or the future value. p = $550 r = 0.09 n = 12 t = 6 f = p(1 + \\frac{r}{n})^{nt} f = $? round to the nearest cent

if $550 are deposited into an account with 9% interest rate, compounded monthly, what is the balance after 6 years? solve for f, or the future value. p = $550 r = 0.09 n = 12 t = 6 f = p(1 + \\frac{r}{n})^{nt} f = $? round to the nearest cent

Answer

Explanation:

Step1: Substitute values into formula

Substitute $P = 550$, $r=0.09$, $n = 12$, $t = 6$ into $F=P(1+\frac{r}{n})^{nt}$. $F=550(1 +\frac{0.09}{12})^{12\times6}$

Step2: Calculate the value inside the parentheses

First, calculate $\frac{0.09}{12}=0.0075$, then $1+\frac{0.09}{12}=1 + 0.0075=1.0075$.

Step3: Calculate the exponent

Next, calculate $nt=12\times6 = 72$.

Step4: Calculate the power

Then, calculate $(1.0075)^{72}$. Using a calculator, $(1.0075)^{72}\approx1.71255$.

Step5: Calculate the future - value

Finally, calculate $F = 550\times1.71255=941.9025\approx941.90$.

Answer:

$941.90$