https://file.aiquickdraw.com/mathbot/file/172764437807833jzt3sz.jpg

Let's go through the problems you uploaded, one by one, using the simple interest formula given in the image:

The formula is:

\[
A = P + Prt
\]

Or simplified:

\[
A = P(1 + rt)
\]

Where:
- \( A \) is the total amount in the account.
- \( P \) is the initial investment (principal).
- \( r \) is the annual interest rate (in decimal form).
- \( t \) is the time in years.

### Question 9:
**Find the value for \( A \) if \( P = 2000 \), \( r = 0.01 \), and \( t = 5 \).**

Using the formula:

\[
A = P(1 + rt)
\]

Substituting the values:

\[
A = 2000 \times (1 + (0.01 \times 5))
\]

Let me calculate that:

\[
A = 2000 \times (1 + 0.05) = 2000 \times 1.05 = 2100
\]

So, the value for \( A \) is **2100**.

---

### Question 10:
**Find \( t \) if \( A = 2200 \), \( P = 2000 \), and \( r = 0.01 \).**

Using the formula:

\[
A = P(1 + rt)
\]

Substitute the given values:

\[
2200 = 2000 \times (1 + 0.01t)
\]

Divide both sides by 2000:

\[
\frac{2200}{2000} = 1 + 0.01t
\]

Simplifying:

\[
1.1 = 1 + 0.01t
\]

Subtract 1 from both sides:

\[
0.1 = 0.01t
\]

Now, divide both sides by 0.01:

\[
t = \frac{0.1}{0.01} = 10
\]

So, \( t = 10 \) years.

---

### Question 11:
**Solve for \( t \) in terms of \( A \), \( P \), and \( r \).**

Start with the formula:

\[
A = P(1 + rt)
\]

Divide both sides by \( P \):

\[
\frac{A}{P} = 1 + rt
\]

Subtract 1 from both sides:

\[
\frac{A}{P} - 1 = rt
\]

Now, divide by \( r \):

\[
t = \frac{\frac{A}{P} - 1}{r}
\]

So, the formula for \( t \) is:

\[
t = \frac{A - P}{Pr}
\]

---

### Question 12:
**Solve for \( P \) in terms of \( A \), \( r \), and \( t \).**

Start with the formula:

\[
A = P(1 + rt)
\]

To isolate \( P \), divide both sides by \( (1 + rt) \):

\[
P = \frac{A}{1 + rt}
\]

So, \( P \) is:

\[
P = \frac{A}{1 + rt}
\]

---

Would you like further details on any of these solutions, or have any specific questions?

### Related Questions:
1. How does the simple interest formula differ from compound interest?
2. If the interest rate doubles, how will that affect the total amount \( A \)?
3. What happens to the total amount if the time \( t \) is halved?
4. Can you graph the relationship between \( A \) and \( t \) for different interest rates?
5. How would you calculate the interest earned, separately from the total amount?

### Tip:
Always convert the interest rate into its decimal form (by dividing the percentage by 100) before using it in formulas.

Find A if P = 2000, r = 0.01, and t = 5. Find t if A = 2200, P = 2000, and r = 0.01. Solve for t in terms of A, P, and r. Solve for P in terms of A, r, and t.

Learn how to calculate the amount (A), time (t), and principal (P) using the simple interest formula. Explore examples like finding A when P = 2000, r = 0.01, and t = 5, and solving for t when A = 2200. Ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation