BUNGA MAJEMUK APLIKASI DERET GEOMETRI MATEMATIKA WAJIB KELAS XI KURIKULUM MERDEKA VIDEO 2

Summary

This video covers the topic of compound interest, explaining how to calculate the amount of interest over different periods using formulas. The presenter walks through the process step-by-step, offering two methods to determine compound interest: manually using a table and an alternative approach with a formula. Various examples are given, such as calculating interest on a savings account with 10% annual interest, showing the final capital after multiple years, and how to calculate the total interest over a specified period. The video concludes with a final example of calculating compound interest for 6 years on a 5 million Rupiah investment.

Takeaways

• 😀 The compound interest formula is used to calculate the amount of interest earned on an investment over time.
• 😀 The general compound interest formula is: M_N = M_0 * (1 + i)^N, where M_N is the final capital, M_0 is the initial capital, i is the interest rate per period, and N is the number of periods.
• 😀 Compound interest is calculated by adding interest to the initial capital, which then earns interest itself in subsequent periods.
• 😀 The amount of compound interest for a specific period can be found by subtracting the previous period's capital from the final capital, i.e., B_N = M_N - M_(N-1).
• 😀 The compound interest formula can be simplified as: B_N = M_0 * i * (1 + i)^(N-1), where B_N is the interest for the N-th period.
• 😀 A practical example demonstrates how interest is calculated manually over three years, showing how interest accumulates each year based on the growing capital.
• 😀 Using the formula, the same results can be achieved more efficiently without manually calculating each year's interest.
• 😀 For example, Dani’s savings of Rp 1 million with 10% annual interest result in an interest of Rp 100,000 at the end of the first year, Rp 110,000 at the end of the second year, and Rp 121,000 at the end of the third year.
• 😀 The formula-based approach gives the same results as the manual calculation, ensuring the accuracy and reliability of the compound interest formula.
• 😀 In a more complex example, after 6 years of compounding at 10% annual interest, the final capital for an initial investment of Rp 5 million is Rp 8,857,805, with total interest earned amounting to Rp 3,857,805.

Q & A

What is the main topic discussed in the script?

The main topic is compound interest and how to calculate it, including examples of calculating interest over multiple years.

What is the formula for determining the amount of compound interest?

The amount of compound interest can be determined by the formula: BN = i * (1 + i)^(n-1) * m0, where BN is the interest for the nth period, i is the interest rate per period, and m0 is the initial capital.

How does the script explain the calculation of compound interest for each year?

The script explains how the interest is calculated yearly by adding the interest to the previous capital and then recalculating for the next year. It provides a step-by-step breakdown for the first three years of savings.

What is the compound interest rate used in the examples provided?

The compound interest rate used in the examples is 10% per year, represented as 0.1 in decimal form.

How do you calculate the interest for the first year in the example?

To calculate the interest for the first year, multiply the initial capital (Rp1,000,000) by the interest rate (0.1). The interest for the first year is Rp100,000.

What happens in the second year of the compound interest example?

In the second year, the interest is calculated by multiplying the capital at the end of the first year (Rp1,100,000) by the interest rate (0.1), resulting in Rp110,000 interest for the second year.

How does compound interest differ from simple interest in the script's explanation?

Compound interest is calculated on both the principal and the accumulated interest, which causes the interest to grow over time. In contrast, simple interest is only calculated on the initial capital.

What formula is used to calculate the total interest over multiple years?

The total interest over multiple years is calculated using the formula: Total interest = Final capital - Initial capital.

What is the final capital after 6 years in the last example?

After 6 years, the final capital is calculated as Rp8,857,805, based on an initial capital of Rp5,000,000 and a 10% annual compound interest rate.

What is the total interest earned after 6 years in the final example?

The total interest earned after 6 years is Rp3,857,805, calculated by subtracting the initial capital of Rp5,000,000 from the final capital of Rp8,857,805.