I see the math problems in your uploaded image. I will solve each one step by step below:

9. Find the time to accumulate an interest of ₱10,200 when ₱85,000 is invested at 4% simple interest.

The formula for simple interest is:
$I = P \cdot r \cdot t$
Where:

• $I = ₱10,200$
• $P = ₱85,000$
• $r = 4\% = 0.04$
• $t = \text{time in years}$

Rearranging for $t$:
$t = \frac{I}{P \cdot r}$
$t = \frac{10,200}{85,000 \cdot 0.04} = \frac{10,200}{3,400} = 3 \, \text{years}$

Answer: $t = 3 \, \text{years}$

10. Pia repays her loan for ₱40,250. If the loan was for 15 months at 12% interest, how much was the principal?

The total amount $A$ is given by:
$A = P \cdot (1 + r \cdot t)$
Where:

• $A = ₱40,250$
• $r = 12\% = 0.12$
• $t = \frac{15}{12} = 1.25 \, \text{years}$

Rearranging for $P$:
$P = \frac{A}{1 + r \cdot t}$
$P = \frac{40,250}{1 + (0.12 \cdot 1.25)} = \frac{40,250}{1 + 0.15} = \frac{40,250}{1.15} = ₱35,000$

Answer: The principal was $₱35,000$.

11. A credit union charges ₱600 interest for the use of ₱12,000 for 90 days. What simple interest rate is in effect?

The formula for interest is:
$I = P \cdot r \cdot t$
Where:

• $I = ₱600$
• $P = ₱12,000$
• $t = \frac{90}{365} = 0.2466 \, \text{years}$

Rearranging for $r$:
$r = \frac{I}{P \cdot t}$
$r = \frac{600}{12,000 \cdot 0.2466} = \frac{600}{2,959.2} = 0.2027 = 20.27\%$

Answer: The simple interest rate is $20.27\%$.

12. If Jessica loaned ₱300,000 from a bank charging 9% simple interest, how much would she pay at the end of three years?

The total amount $A$ is given by:
$A = P \cdot (1 + r \cdot t)$
Where:

• $P = ₱300,000$
• $r = 9\% = 0.09$
• $t = 3 \, \text{years}$

Substituting:
$A = 300,000 \cdot (1 + 0.09 \cdot 3) = 300,000 \cdot (1 + 0.27) = 300,000 \cdot 1.27 = ₱381,000$

Answer: Jessica would pay $₱381,000$.

3. How much will Eric receive if he invested ₱100,000 for one year and three months at 15% interest?

The time $t$ is:
$t = 1 \, \text{year} + \frac{3}{12} \, \text{years} = 1.25 \, \text{years}$
The total amount $A$ is:
$A = P \cdot (1 + r \cdot t)$
Where:

• $P = ₱100,000$
• $r = 15\% = 0.15$
• $t = 1.25 \, \text{years}$

Substituting:
$A = 100,000 \cdot (1 + 0.15 \cdot 1.25) = 100,000 \cdot (1 + 0.1875) = 100,000 \cdot 1.1875 = ₱118,750$

Answer: Eric will receive $₱118,750$.

Let me know if you'd like further details on any of these!

Here are 5 related questions to expand your learning:

1. What is the formula for compound interest, and how does it differ from simple interest?
2. How would the answer to Question 9 change if the rate was compounded annually instead of being simple interest?
3. How do we calculate the effective annual rate (EAR) for interest rates?
4. If a loan had a variable interest rate that changed annually, how would you calculate the total payment?
5. How does inflation impact the real value of interest earned on investments?

Tip: Always double-check the time unit (e.g., years, months, days) when solving interest-related problems—it’s a common source of mistakes!