Let’s solve these problems one by one using the formula for Simple Interest:

Formula:

$I = P \times r \times t$ Where:

• $I$: Simple interest
• $P$: Principal amount
• $r$: Annual interest rate (in decimal form)
• $t$: Time (in years)

Problem 1:

Rommel takes a loan of $\text{₱5,000}$ at 9.5% simple interest. Calculate the annual interest.

Given:

• $P = 5000$
• $r = 9.5\% = 0.095$
• $t = 1$ year

$I = P \times r \times t = 5000 \times 0.095 \times 1 = \text{₱475}$

Answer: The annual interest is ₱475.

Problem 2:

Mary borrowed $\text{₱800,000}$ at 11.5% interest and paid $\text{₱9,500}$ interest. Find the time.

Given:

• $P = 800,000$
• $r = 11.5\% = 0.115$
• $I = 9,500$

Rearrange the formula to find $t$: $t = \frac{I}{P \times r} = \frac{9500}{800,000 \times 0.115}$

$t = \frac{9500}{92,000} = 0.1033 \, \text{years} \, (\approx 1.24 \, \text{months})$

Answer: The loan term is approximately 0.1033 years or 1.24 months.

Problem 3:

Dianne paid $\text{₱4,450}$ interest for 1.5 years at 15% per annum. What was the original loan?

Given:

• $I = 4,450$
• $r = 15\% = 0.15$
• $t = 1.5$

Rearrange the formula to find $P$: $P = \frac{I}{r \times t} = \frac{4450}{0.15 \times 1.5}$

$P = \frac{4450}{0.225} = \text{₱19,778}$

Answer: The original loan was ₱19,778.

Problem 4:

Darryl borrowed $\text{₱156,300}$ at 9% interest and paid $\text{₱4,500}$ interest. How long did he use the money?

Given:

• $P = 156,300$
• $r = 9\% = 0.09$
• $I = 4,500$

Rearrange the formula to find $t$: $t = \frac{I}{P \times r} = \frac{4500}{156,300 \times 0.09}$

$t = \frac{4500}{14,067} \approx 0.32 \, \text{years or 3.84 months}$

Answer: He used the money for approximately 0.32 years or 3.84 months.

Problem 5:

At what rate of interest did Annie invest $\text{₱23,500}$ to earn $\text{₱3,525}$ in 4 years?

Given:

• $P = 23,500$
• $I = 3,525$
• $t = 4$

Rearrange the formula to find $r$: $r = \frac{I}{P \times t} = \frac{3525}{23,500 \times 4}$

$r = \frac{3525}{94,000} = 0.0375 = 3.75\%$

Answer: The rate of interest was 3.75%.

Do you need further clarifications or detailed steps for any problem? Here are related questions for you:

1. How can you convert months into years when solving simple interest problems?
2. How does compound interest differ from simple interest?
3. Can you calculate the total amount paid after adding principal and interest for these cases?
4. How do you compute interest if the rate changes during the loan period?
5. What would happen if the time or interest rate were fractions?

Tip: Always double-check the formula rearrangement when solving for a specific variable.