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?

Explanation:

Step1: Identify the formula for compound interest

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 (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for in years.

Assuming the interest is compounded annually, $n = 1$.

Step2: Convert the interest rate to decimal

The annual interest rate $r = 9\% = 0.09$.

Step3: Substitute the values into the formula

We have $P = 3600$, $r = 0.09$, $n = 1$, and $t = 25$.
Substituting these values into the formula:
$$A = 3600(1 + \frac{0.09}{1})^{1\times25}$$
$$A = 3600(1.09)^{25}$$

Step4: Calculate $(1.09)^{25}$

Using a calculator, $(1.09)^{25} \approx 8.623081$

Step5: Calculate $A$

$$A = 3600\times8.623081 \approx 31043.09$$

Answer:

The amount in the account after 25 years, to the nearest cent, is $\$31043.09$.