Question

question 3600 dollars is placed in an account with an annual interest rate of 9%. how much will be in the account after 25 years, to the nearest cent? answer attempt 1 out of 2 submit answer

Explanation:

Step1: Identify the formula for compound interest

The formula for compound interest (assuming annual compounding, which is common if not specified otherwise) is $A = P(1 + r)^t$, 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 (decimal).
• $t$ is the time the money is invested for in years.

Here, $P = 3600$ dollars, $r = 9\% = 0.09$, and $t = 25$ years.

Step2: Substitute the values into the formula

Substitute $P = 3600$, $r = 0.09$, and $t = 25$ into the formula:
$$A = 3600(1 + 0.09)^{25}$$

Step3: Calculate $(1 + 0.09)^{25}$

First, calculate $1 + 0.09 = 1.09$. Then, calculate $1.09^{25}$. Using a calculator, $1.09^{25}\approx 8.62308066$.

Step4: Calculate the final amount

Multiply the principal by the result from Step 3:
$$A = 3600\times 8.62308066 \approx 31043.09$$

Answer:

$\$31043.09$