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**

$ 1500$1500

2.3 %2.3%

dailydaily

2.5 years2.5 years

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Part 1

**a.** Find how much money there will be in the account after the given number of years.​ (Assume 365 days in a​ year.)

The amount of money in the account after 

2.52.5 

years is 

​$enter your response here.

​(Round to the nearest cent as​ needed.)

To find how much money there will be in the account after 2.5 years, given the principal, interest rate, and compounding frequency, we 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 $t$ years.
- $P$ is the principal (initial amount).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the number of years.

In this problem:
- $P = 1500$
- $r = 2.3\% = 0.023$
- $n = 365$ (since the interest is compounded daily)
- $t = 2.5$ years

Now, let's substitute these values into the formula and calculate the amount $A$.The amount of money in the account after 2.5 years will be approximately $1588.78, rounded to the nearest cent.

Do you want further details or have any questions? 

Here are 5 related questions to explore:
1. How does the compounding frequency affect the final amount?
2. What if the interest was compounded monthly instead of daily?
3. How would the result change if the interest rate increased to 3%?
4. Can you compare simple interest and compound interest for this scenario?
5. What happens if the deposit time is extended to 5 years?

**Tip:** Compounding more frequently generally results in higher final amounts due to the interest earning interest more often.

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Find how much money there will be in the account after the given number of years. Principal: $1500, Rate: 2.3%, Compounded: daily, Time: 2.5 years.

Calculate the compound interest on a principal of $1500 with an interest rate of 2.3%, compounded daily over 2.5 years. Learn how to apply the compound interest formula to find the total amount in the account. This is a detailed solution, ideal for high school students in Grades 10-12.

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