Zinsrechnung - Kapital berechnen | Formel umstellen - viele Übungen | Lehrerschmidt

Summary

In this educational video, the instructor walks students through the concept of calculating capital in interest rates, focusing on the process of rearranging the formula for calculating interest. The video includes examples with various time periods (days, months) and interest rates, demonstrating how to solve for the principal amount (capital) by using the formula. Key tips for solving the problems, such as simplifying calculations with a calculator or by reducing fractions, are shared. The instructor emphasizes understanding the formulas and how they adapt for different time units like days or months.

Takeaways

• 😀 The formula for calculating capital in interest calculation is K = Z × 100 ÷ (P × t), where Z is the interest amount, P is the percentage, and t is the time period (in days or months).
• 😀 When working with interest calculations for days, the formula is extended with a factor of 360 days, while for months, it is extended with 12 months.
• 😀 The formula is rearranged to solve for the capital (K), making it the primary focus of the calculation.
• 😀 In the first example, the capital is calculated by inputting values for interest (Z), percentage (P), and time period (t), yielding a result of 30,000 EUR.
• 😀 For calculations involving interest for 100 days at a 1.5% interest rate and 220 EUR interest, the capital is found to be 52,800 EUR using the same formula with day-based adjustments.
• 😀 In the third example, the capital is calculated with a 220-day period, a 2.5% interest rate, and 280 EUR interest, yielding 18,300 EUR.
• 😀 The formula can be applied to various timeframes, such as 3 months or 36 months, and different interest rates, like 2%, depending on the problem at hand.
• 😀 The process emphasizes the importance of using a calculator and the potential for shortcuts in calculations by simplifying fractions and terms in the formula.
• 😀 For monthly-based interest calculations, the formula is adjusted to use 12 months, as demonstrated in the examples involving 90 EUR interest over 3 months, resulting in 18,000 EUR capital.
• 😀 The final example shows how a 6-month period with a 2% interest rate results in a capital of 14,000 EUR from 140 EUR interest, using the same formula and simplifications.

Q & A

What is the main goal of the lesson in the script?

The main goal of the lesson is to teach how to calculate the capital (K) in interest calculations, using a rearranged formula based on given interest (Z), time (T), and percentage rate (P).

What formula is introduced for calculating capital (K) in the lesson?

The formula introduced for calculating capital (K) is K = (Z × 100 × T) / (P × 360), where Z is the interest, P is the percentage rate, and T is the time period, using 360 days for daily interest calculations.

Why is the number 360 used in the formula when calculating with days?

The number 360 is used in the formula to standardize the number of days in a year for interest calculations, as it is a common practice in finance to simplify calculations using a 360-day year.

How does the formula change when calculating with months instead of days?

When calculating with months, the formula is adjusted to K = (Z × 100 × 12) / (P × T), where 12 is used instead of 360 to account for the number of months in a year.

What does the instructor emphasize about using a calculator in the lesson?

The instructor emphasizes that while a calculator can be used to simplify the calculations, it is important to check if shortcuts, such as canceling out terms or simplifying fractions, can be used to make the process faster.

What should students focus on when rearranging the formula to find the capital?

Students should focus on isolating the capital (K) in the formula, removing the interest (Z), percentage rate (P), and time (T) by using algebraic steps, such as multiplying and dividing appropriately.

In the example with 120 days, a 2% interest rate, and 200 euros in interest, what is the capital (K)?

The capital (K) in the example with 120 days, a 2% interest rate, and 200 euros in interest is 30,000 euros.

What steps does the instructor take to calculate the capital when the interest is given in the example with 100 days and a 1.5% interest rate?

The instructor uses the formula for capital, then substitutes the values for the interest (220 euros), the time (100 days), and the interest rate (1.5%). After that, they simplify the calculation, either by canceling out terms or directly entering it into a calculator.

What is the significance of expanding the formula with 360 when using days and 12 when using months?

Expanding the formula with 360 when using days and 12 when using months ensures that the time component is correctly factored into the calculation, maintaining consistency in the units for both types of interest calculations.

What is the result of calculating the capital in the last example with 6 months, 2% interest, and 140 euros in interest?

The result of calculating the capital in the last example with 6 months, 2% interest, and 140 euros in interest is 14,000 euros.