if $900 are deposited into an account with a 5.5% interest rate, compounded quarterly, what is the balance…

if $900 are deposited into an account with a 5.5% interest rate, compounded quarterly, what is the balance after 20 years? f = $? f = p(1 + \\frac{r}{n})^{nt} round to the nearest cent.

if $900 are deposited into an account with a 5.5% interest rate, compounded quarterly, what is the balance after 20 years? f = $? f = p(1 + \\frac{r}{n})^{nt} round to the nearest cent.

Answer

Explanation:

Step1: Identify the values

$P = 900$, $r=0.055$, $n = 4$ (quarter - ly compounding), $t = 20$

Step2: Substitute into the compound - interest formula

$F=P(1 +\frac{r}{n})^{nt}=900(1+\frac{0.055}{4})^{4\times20}$

Step3: Calculate the value inside the parentheses

$1+\frac{0.055}{4}=1 + 0.01375=1.01375$

Step4: Calculate the exponent

$4\times20 = 80$

Step5: Calculate the power

$(1.01375)^{80}\approx2.95997$

Step6: Calculate the final amount

$F=900\times2.95997 = 2663.973\approx2663.97$

Answer:

$2663.97$