if $500 are deposited into an account with a 4.5% interest rate, compounded annually, what is the balance…

if $500 are deposited into an account with a 4.5% interest rate, compounded annually, what is the balance after 6 years? f = $? f = p(1 + \\frac{r}{n})^{nt} round to the nearest cent.

if $500 are deposited into an account with a 4.5% interest rate, compounded annually, what is the balance after 6 years? f = $? f = p(1 + \\frac{r}{n})^{nt} round to the nearest cent.

Answer

Explanation:

Step1: Identify the values

$P = 500$, $r=0.045$ (since $4.5%=0.045$), $n = 1$ (compounded annually), $t = 6$

Step2: Substitute into the compound - interest formula

$F=P(1 +\frac{r}{n})^{nt}=500(1+\frac{0.045}{1})^{1\times6}$

Step3: Calculate the value inside the parentheses

$1+\frac{0.045}{1}=1 + 0.045=1.045$

Step4: Calculate the exponent

$nt=1\times6 = 6$

Step5: Calculate the power

$(1.045)^{6}\approx1.30226$

Step6: Calculate the final amount

$F = 500\times1.30226=651.13$

Answer:

$651.13$