Question

3400 dollars is placed in an account with an annual interest rate of 7.5%. how much will be in the account after 17 years, to the nearest cent?

Explanation:

Step1: Identify compound interest formula

Assuming annual compounding (standard for such problems), the formula is:
$$A = P(1 + r)^t$$
Where $A$ = final amount, $P$ = principal, $r$ = annual interest rate (decimal), $t$ = time in years.

Step2: Convert rate to decimal

$$r = \frac{7.5}{100} = 0.075$$

Step3: Plug values into formula

Substitute $P=3400$, $r=0.075$, $t=17$:
$$A = 3400(1 + 0.075)^{17}$$

Step4: Calculate the growth factor

$$(1.075)^{17} \approx 3.42478$$

Step5: Compute final amount

$$A = 3400 \times 3.42478 \approx 11644.25$$

Answer:

$\$11644.25$