Question

find the final amount of money in an account if $6,700 is deposited at 4% interest compounded weekly and the money is left for 6 years. the final amount is $ \boxed{}. 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 each variable

• Given that $P=\$6700$.
• The annual interest rate $r = 4\%=0.04$.
• Since interest is compounded weekly, and there are 52 weeks in a year, $n = 52$.
• The time $t = 6$ years.

Step3: Substitute the values into the formula

$$
LATEXBLOCK0
$$

First, calculate the value inside the parentheses: $\frac{0.04}{52}\approx0.0007692$, and $1 + 0.0007692=1.0007692$.

Then, calculate the exponent: $52\times6 = 312$.

Now, calculate $(1.0007692)^{312}$. Using a calculator, $(1.0007692)^{312}\approx1.258467$.

Finally, multiply by the principal: $A = 6700\times1.258467\approx8431.73$

Answer:

8431.73