find the final amount of money in an account if $8,300 is deposited at 3.5% interest compounded weekly and…

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

Step2: Convert values to appropriate form

Given $P = 8300$, $r=0.035$ (since $3.5%=0.035$), $n = 52$ (compounded weekly), and $t = 6$.

Step3: Substitute values into the formula

$A=8300(1 +\frac{0.035}{52})^{52\times6}$. First, calculate $\frac{0.035}{52}\approx0.000673$. Then $1+\frac{0.035}{52}=1 + 0.000673=1.000673$. Next, $52\times6 = 312$. So $A = 8300\times(1.000673)^{312}$. Calculate $(1.000673)^{312}\approx1.23377$. Then $A=8300\times1.23377\approx10240.29$.

Answer:

$10240.29$