Question

7700 dollars is placed in an account with an annual interest rate of 5.75%. how much will be in the account after 24 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
• $P = 7700$ (principal)
• $r = 0.0575$ (annual rate)
• $t = 24$ (time in years)

Step2: Substitute values into formula

$$A = 7700(1 + 0.0575)^{24}$$

Step3: Calculate the growth factor

First compute $1.0575^{24} \approx 3.8881$

Step4: Compute final amount

$$A = 7700 \times 3.8881 \approx 29938.37$$

Answer:

$\$29938.37$