question 3600 dollars is placed in an account with an annual interest rate of 9%. how much will be in the…

Explanation:

Step1: Identify the formula for compound interest (assuming compound interest, as simple interest isn't specified and compound is common for long-term accounts)

The compound - interest formula 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. If not specified, we assume $n = 1$ (annual compounding).
• $t$ is the time the money is invested for in years.

Given:

• $P=$3600$
• $r = 9%=0.09$
• $n = 1$ (assuming annual compounding)
• $t = 25$ years

Step2: Substitute the values into the formula

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

$A=3600\times(1+\frac{0.09}{1})^{1\times25}$

First, calculate the value inside the parentheses: $1+\frac{0.09}{1}=1 + 0.09=1.09$

Then, calculate the exponent: $1\times25 = 25$

So, $A = 3600\times(1.09)^{25}$

Step3: Calculate $(1.09)^{25}$

Using a calculator, $(1.09)^{25}\approx8.62308066$

Step4: Calculate the amount $A$

Multiply $3600$ by $8.62308066$:

$A=3600\times8.62308066\approx31043.09$

Answer:

$$31043.09$