บทที่ 3 ดอกเบี้ยและมูลค่าของเงิน ep.3

Summary

In this video, the process of calculating the annual interest rate for a compound interest scenario is explained step-by-step. The example involves a deposit of 10,000 Baht in a bank that compounds interest quarterly, leading to a final balance of 10,938 Baht after 3 years. The script walks through the formula for compound interest, breaking it down to find the interest rate per year. By isolating the rate and converting it to a percentage, the final result reveals an annual interest rate of approximately 3%. This practical approach helps viewers understand how compound interest works in real-life situations.

Takeaways

• 😀 The script explains a compound interest calculation involving a 10,000 THB deposit with quarterly compounding.
• 😀 The formula used is: A = P(1 + r/k)^(kn), where A is the final amount, P is the principal, r is the interest rate, k is the number of compounding periods per year, and n is the number of years.
• 😀 The final amount after 3 years is 10,938 THB, which is used to calculate the interest rate.
• 😀 Interest is compounded every 3 months, so the number of periods per year (k) is 4.
• 😀 The time period for the calculation is 3 years, so n = 3.
• 😀 The formula is rearranged to isolate the interest rate (r). The intermediate steps include taking the 12th root and solving for r.
• 😀 The interest rate (r) is found to be approximately 0.03 or 3%.
• 😀 The script emphasizes using a calculator for more accurate calculations, especially for extracting roots and performing complex operations.
• 😀 The script notes that rounding is necessary because the 12th root of 1.0938 doesn’t result in a simple number.
• 😀 The final answer is approximately 3% annual interest, which is the required rate for this compound interest scenario.
• 😀 The explanation encourages practicing calculations with a calculator to gain familiarity with compound interest formulas.

Q & A

What is the main topic of the script?

The script explains how to calculate the annual interest rate on an investment that is compounded quarterly using a given final amount and initial deposit.

What formula is used in the script to solve for the interest rate?

The formula used is the compound interest formula: A = P * (1 + r/k)^(k * n), where A is the final amount, P is the initial deposit, r is the annual interest rate, k is the number of compounding periods per year, and n is the number of years.

What does the symbol 'k' represent in the formula?

'k' represents the number of times the interest is compounded per year. In this case, since the interest is compounded quarterly, k = 4.

What is the final balance after 3 years according to the script?

The final balance after 3 years is 10,938 Baht.

How do you calculate the interest rate from the formula?

To calculate the interest rate, first substitute the given values into the compound interest formula, then solve for 'r'. This involves isolating 'r' by taking the 12th root of the equation and solving for 'r'.

Why is the 12th root used in the calculation?

The 12th root is used because the interest is compounded quarterly, and the formula has the exponent (k * n) which equals 12 (since k = 4 and n = 3 years). Taking the 12th root removes the exponent and simplifies the equation.

What is the value of the interest rate after calculation?

After calculation, the interest rate is approximately 3% per year.

What is the purpose of multiplying the result by 100 in the calculation?

Multiplying the result by 100 converts the decimal value of the interest rate to a percentage, which is the standard way of expressing interest rates.

How was the value 1.0938 derived in the script?

The value 1.0938 was derived by dividing the final amount (10,938 Baht) by the initial deposit (10,000 Baht), which results in 1.0938.

What step involves isolating the interest rate, and how is it done?

The step involving isolating the interest rate occurs after the 12th root has been taken. At this point, you subtract 1 from both sides of the equation to solve for r, then multiply by 4 to find the annual interest rate.