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Part 1
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
$ 2500
0.7 %
quarterly
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. 
The amount of money in the account after 5 years is ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)

To solve this problem, we'll use the compound interest formula:

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

Where:
- $ A $ is the amount of money in the account after time $ t $,
- $ P $ is the principal (initial deposit) which is $2500,
- $ r $ is the annual interest rate (as a decimal) which is 0.7% or 0.007,
- $ n $ is the number of times the interest is compounded per year (quarterly means $ n = 4 $),
- $ t $ is the number of years, which is 5.

Now, let's substitute the values into the formula:

\[
A = 2500 \left(1 + \frac{0.007}{4}\right)^{4 \times 5}
\]

\[
A = 2500 \left(1 + 0.00175\right)^{20}
\]

\[
A = 2500 \left(1.00175\right)^{20}
\]

Now calculate the power and then the final amount:

\[
A \approx 2500 \times 1.035522
\]

\[
A \approx 2588.80
\]

Thus, the amount of money in the account after 5 years is approximately **$2588.80**.

Do you need more details on this process? Also, here are 5 related questions:

1. How would the amount change if the interest were compounded monthly instead of quarterly?
2. What would the amount be if the rate was 1% instead of 0.7%?
3. How does increasing the time to 10 years affect the amount?
4. What is the difference in total interest earned if the principal was $5000 instead of $2500?
5. What happens to the final amount if the interest rate was compounded annually instead of quarterly?

**Tip:** Compound interest grows faster when the interest is compounded more frequently.

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: $2500, Rate: 0.7%, Compounded: quarterly, Time: 5 years. a. Find how much money there will be in the account after the given number of years.

Discover how to calculate compound interest for a principal of $2500 deposited at a 0.7% interest rate compounded quarterly over 5 years. This example demonstrates key finance concepts like exponential growth and compound interest formulas. Ideal for students in Grades 9-12.

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