find the amount in the account for the given principal, interest rate, time, and compounding period. p =…

find the amount in the account for the given principal, interest rate, time, and compounding period. p = $3,520, r = 5.5%, t = 24 years; compounded monthly a = $ (type an integer or decimal rounded to the nearest cent as needed.)

find the amount in the account for the given principal, interest rate, time, and compounding period. p = $3,520, r = 5.5%, t = 24 years; compounded monthly a = $ (type an integer or decimal rounded to the nearest cent as needed.)

Answer

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 compounded per year, and $t$ is the number of years.

Step2: Convert the interest rate to decimal

Given $r = 5.5%=0.055$.

Step3: Determine the value of $n$

Since it is compounded monthly, $n = 12$.

Step4: Substitute the values into the formula

We have $P = 3520$, $r = 0.055$, $n = 12$, and $t = 24$. Substitute these into the formula: [ \begin{align*} A&=3520\left(1 +\frac{0.055}{12}\right)^{12\times24}\ &=3520\left(1+\frac{0.055}{12}\right)^{288} \end{align*} ] First, calculate $1+\frac{0.055}{12}=1 + 0.0045833\approx1.0045833$. Then, $(1.0045833)^{288}\approx3.81777$. Finally, $A = 3520\times3.81777\approx13448.55$.

Answer:

$13448.55$