find the final amount of money in an account if $900 is deposited at 6.5% interest compounded weekly and the…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ 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=$900$, $r = 6.5%=0.065$, since it is compounded weekly, $n = 52$, and $t = 9$ years.

Step3: Substitute values into the formula

$A=900(1 +\frac{0.065}{52})^{52\times9}$. First, calculate the value inside the parentheses: $\frac{0.065}{52}=0.00125$, then $1+\frac{0.065}{52}=1 + 0.00125=1.00125$. Next, calculate the exponent: $52\times9 = 468$. So, $A = 900\times(1.00125)^{468}$.

Step4: Calculate the final amount

$(1.00125)^{468}\approx1.89777$. Then $A=900\times1.89777=$1707.993$. Rounding to 2 decimal places, $A\approx$1707.99$.

Answer:

$1707.99$