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.