if a savings account of $6800 is compounded quarterly at 8.33 % annual interest, how much will the account…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert the given values to the appropriate form

Given $P=$6800$, $r = 8.33%=0.0833$, $n = 4$ (compounded quarterly), and $t=\frac{29}{12}$ years.

Step3: Substitute the values into the formula

$A = 6800(1+\frac{0.0833}{4})^{4\times\frac{29}{12}}$. First, calculate the value inside the parentheses: $\frac{0.0833}{4}=0.020825$, so $1+\frac{0.0833}{4}=1 + 0.020825=1.020825$. Next, calculate the exponent: $4\times\frac{29}{12}=\frac{29}{3}\approx9.67$. Then, $A = 6800\times(1.020825)^{\frac{29}{3}}$. $(1.020825)^{\frac{29}{3}}\approx1.21077$. $A = 6800\times1.21077=$8233.24$.

Answer:

$8233.24$