Question

assignment 6.1 exponential functions
score: 6.95/10 answered: 9/10
question 10
find the final amount of money in an account if $8,400 is deposited at 6.5% interest compounded weekly and the money is left for 8 years. assume there are 52 weeks in a year.
the final amount is $ . round answer to 2 decimal places

Explanation:

Step1: Recall the compound - interest formula

The formula for compound interest 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.
• $t$ is the time the money is invested for in years.

Step2: Identify the values of $P$, $r$, $n$, and $t$

• Given that $P=\$8400$.
• The annual interest rate $r = 6.5\%=0.065$.
• Since interest is compounded weekly and there are 52 weeks in a year, $n = 52$.
• The time $t = 8$ years.

Step3: Substitute the values into the formula

First, calculate the value of $\frac{r}{n}$: $\frac{0.065}{52}=0.00125$.
Then, calculate the value of $nt$: $nt=52\times8 = 416$.
Next, calculate $(1 + \frac{r}{n})$: $1+0.00125 = 1.00125$.
Then, calculate $(1+\frac{r}{n})^{nt}$: $(1.00125)^{416}$. We can use a calculator to find that $(1.00125)^{416}\approx1.588621$.
Finally, calculate $A$: $A=P(1 + \frac{r}{n})^{nt}=8400\times1.588621\approx13344.42$.

Answer:

13344.42