Let's solve the two problems presented in the image.

1. Interest and Maturity Value of a Loan

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

• $I$ = Interest
• $P$ = Principal amount = 33,000 PHP
• $r$ = Annual interest rate = 12.5% = 0.125
• $t$ = Time in years = 5 years

Now, calculate the interest: $I = 33,000 \times 0.125 \times 5 = 20,625 \, \text{PHP}$

The maturity value ($A$) is the total amount after the interest is added: $A = P + I = 33,000 + 20,625 = 53,625 \, \text{PHP}$

Thus, the interest is 20,625 PHP, and the maturity value is 53,625 PHP.

2. Finding Interest Rate and Time

Part A: At what simple interest per annum will $P_1$ become $P_2$ in 2 years?

This part asks for the rate at which an initial principal $P_1$ becomes $P_2$ after 2 years. The simple interest formula rearranged for rate ($r$) is: $r = \frac{P_2 - P_1}{P_1 \times t}$ Since no specific values for $P_1$ and $P_2$ are given, we keep the formula general for now.

Part B: How long for 1 million pesos to earn 100,000 PHP at 3% per annum?

Here, $P = 1,000,000$ PHP, $I = 100,000$ PHP, and $r = 3\% = 0.03$. The formula for time is: $t = \frac{I}{P \times r}$

Substitute the known values: $t = \frac{100,000}{1,000,000 \times 0.03} = \frac{100,000}{30,000} \approx 3.33 \, \text{years}$

So, it will take approximately 3.33 years to earn 100,000 PHP in interest.

Would you like more details on any of these solutions or have other questions? Here are 5 related questions:

1. How is compound interest different from simple interest?
2. How would the calculation change if the loan period were in months rather than years?
3. What happens to the interest if the rate changes midway through the loan period?
4. Can you calculate the interest if the principal grows over time (e.g., through additional deposits)?
5. How can inflation affect the real value of the maturity amount?

Tip: Always double-check if the interest rate provided is annual, and adjust the formula accordingly if the time is given in months or days.