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 = $500, r = 5%, t = 7 years; compounded quarterly 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 = $500, r = 5%, t = 7 years; compounded quarterly 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 values to appropriate form

Given $P = 500$, $r=0.05$ (since $5%=0.05$), $n = 4$ (compounded quarterly), and $t = 7$.

Step3: Substitute values into the formula

$A=500(1 +\frac{0.05}{4})^{4\times7}=500(1 + 0.0125)^{28}$.

Step4: Calculate the value inside the parentheses

$1+0.0125 = 1.0125$.

Step5: Calculate the exponent part

$(1.0125)^{28}\approx1.412973$.

Step6: Calculate the final amount

$A = 500\times1.412973=706.4865\approx706.49$.

Answer:

$706.49$