The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts​ (a) and​ (b).
Principal
Rate
Compounded
Time
$ 9500
1.5 %
monthly
2 years
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Part 1
a. Find how much money there will be in the account after the given number of years.
The amount of money in the account after 2 years is ​$
  
enter your response here.
​(Round to the nearest hundredth as​ needed.)

To calculate how much money will be in the account after 2 years with monthly compounded interest, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $A$ is the amount of money in the account after time $t$,
- $P$ is the principal amount ($9500),
- $r$ is the annual interest rate (1.5% or 0.015),
- $n$ is the number of times the interest is compounded per year (monthly compounding means $n = 12$),
- $t$ is the time the money is invested for, in years (2 years).

Let's plug in the values:

\[
A = 9500 \left(1 + \frac{0.015}{12}\right)^{12 \times 2}
\]

Now, simplify step-by-step:

\[
A = 9500 \left(1 + 0.00125\right)^{24}
\]
\[
A = 9500 \left(1.00125\right)^{24}
\]
\[
A = 9500 \times 1.030416
\]
\[
A \approx 9788.96
\]

Thus, the amount of money in the account after 2 years is approximately **$9788.96**.

Would you like me to explain any part of this in more detail, or have further questions? 

Here are 5 related questions:
1. How would the amount change if the interest rate was increased to 2%?
2. What would happen if the interest were compounded quarterly instead of monthly?
3. How would the total amount be affected by a longer time, say 5 years?
4. What formula would you use for simple interest instead of compound interest?
5. How does the frequency of compounding influence the final amount?

**Tip:** Increasing the frequency of compounding results in more interest earned over time due to the effect of compounding on previously earned interest.

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Answer parts (a) and (b). Principal: $9500, Rate: 1.5%, Compounded: Monthly, Time: 2 years. Find how much money there will be in the account after the given number of years. (Round to the nearest hundredth as needed.)

Learn how to calculate compound interest for a principal amount of $9500 at an interest rate of 1.5%, compounded monthly for 2 years. This step-by-step solution includes the compound interest formula and applies exponential growth principles to financial mathematics, suitable for high school students in Grades 10-12.

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