SIMPLE INTEREST || GRADE 11 GENERAL MATHEMATICS Q2

Summary

This video lesson focuses on simple interest, covering its definition, calculation, and related formulas. The instructor explains how to compute simple interest, maturity value, and present value using key formulas like I = PRT. Multiple examples and problem-solving exercises demonstrate how to find unknown values like interest, principal, rate, and time. The video also includes a series of practice questions to reinforce understanding, helping viewers apply simple interest calculations to various financial situations. It concludes with a quick review and a multiple-choice quiz to test knowledge.

Takeaways

• 📊 Simple interest is calculated on the principal alone for the entire duration of the loan or investment.
• 🧮 The formula for simple interest is I = P * R * T, where P is the principal, R is the rate, and T is the time in years.
• 💰 The maturity value (or future value) is the sum of the principal and the interest.
• 🔄 To find the principal, interest, or time, you can rearrange the simple interest formula based on the given values.
• 📉 Converting percentages into decimals is essential for calculations (e.g., 2.5% = 0.025).
• ⏳ The duration (T) in years can be fractional if the time period is less than one year (e.g., 9 months = 0.75 years).
• 📈 Interest is calculated based on the principal, rate, and time, and different problems require solving for different unknowns.
• 💸 The future value can be computed using the formula F = P * (1 + R * T).
• 🧾 To solve real-life simple interest problems, identify key values like principal, rate, and time and apply the correct formula.
• 🎯 In a multiple-choice question format, understanding the key formulas helps in solving for different aspects of financial transactions (e.g., interest, principal, future value).

Q & A

What is simple interest?

Simple interest is the interest charged on the principal alone for the entire duration of the loan or investment, calculated at a specific rate over a set time period.

What formula is used to calculate simple interest?

The formula for calculating simple interest is I = P × R × T, where I is the interest, P is the principal amount, R is the rate of interest (in decimal form), and T is the time in years.

How do you calculate the maturity value or future value?

The maturity value (F) or future value is calculated using the formula F = P + I, where P is the principal and I is the interest. Alternatively, you can use the formula F = P × (1 + RT).

How do you convert a percentage rate into a decimal?

To convert a percentage rate into a decimal, divide the percentage by 100. For example, 2.5% becomes 0.025 when converted to a decimal.

How would you find the principal if the interest, rate, and time are known?

The principal (P) can be found using the formula P = I / (R × T), where I is the interest, R is the rate, and T is the time.

What is the interest earned on a principal of 1 million pesos at a rate of 0.25% for one year?

Using the formula I = P × R × T, the interest earned would be 1,000,000 × 0.0025 × 1 = 2,500 pesos.

How do you calculate the rate when the principal, interest, and time are known?

The rate (R) is calculated using the formula R = I / (P × T). For example, if the interest is 157,500 pesos, the principal is 500,000 pesos, and the time is 3 years, R = 157,500 / (500,000 × 3) = 0.105 or 10.5%.

How long will it take for a principal to double at a simple interest rate of 5%?

Using the formula I = P × R × T, and given that the interest is half of the principal (0.5P), the time (T) is calculated as T = 0.5P / (P × 0.05) = 10 years.

What is the maturity value after 5 years if 1 million pesos is deposited at a 0.25% annual simple interest rate?

The maturity value is calculated as F = P + I, where I = P × R × T. So, I = 1,000,000 × 0.0025 × 5 = 12,500 pesos. The maturity value is 1,000,000 + 12,500 = 1,012,500 pesos.

What is the present value of 86,000 pesos at an 8% simple interest rate over 3 years?

The present value (P) is calculated using the formula P = F / (1 + RT), where F is the future value. Substituting the values, P = 86,000 / (1 + 0.08 × 3) = 69,354.84 pesos.