Question

question 6 (10 points)you plan to deposit $77,600 into a savings account that has a 5.31% interest rate compounded monthly. what will be the balance of your savings account after 22 years?use this formula:$a = p(1 + \frac{r}{n})^{nt}$enter the dollar amount rounded to the nearest cent.your answer:

Explanation:

Step1: Define variables

$P = 77600$, $r = 0.0531$, $n = 12$, $t = 22$

Step2: Calculate periodic rate

$\frac{r}{n} = \frac{0.0531}{12} = 0.004425$

Step3: Calculate total periods

$nt = 12 \times 22 = 264$

Step4: Compute growth factor

$(1 + 0.004425)^{264} \approx e^{264 \times \ln(1.004425)} \approx 3.20017$

Step5: Compute final amount

$A = 77600 \times 3.20017$

Answer:

$248333.19$