บทที่ 3 ดอกเบี้ยและมูลค่าของเงิน ep.5 [มูลค่าปัจจุบันและมูลค่าอนาคต]

Summary

This transcript discusses various loan and interest calculation scenarios. The first example involves a loan with compound interest, where the principal is calculated based on a future payment of 40,656 Baht due in two years with an 8% annual interest rate. The second example details a similar calculation for two different payments, totaling 30,000 Baht, due in two and five years, with the same interest rate, compounded quarterly. The script focuses on using standard compound interest formulas to determine the present value of future obligations, providing a clear understanding of financial calculations for loans.

Takeaways

• 😀 A loan is being taken by Wari from Natcha, with the repayment due in 2 years totaling 40,656 Baht at an 8% annual interest rate, compounded annually.
• 😀 The formula for calculating the present value (P) involves multiplying the future value (S) by a factor based on the interest rate (r), compounding frequency (k), and time period (n).
• 😀 To find the present value (P), the formula used is P = S * (1 + r/k) ^ (-kn). This is a standard formula for calculating compound interest with regular compounding periods.
• 😀 For Wari's loan, the calculation using the formula results in a present value (P) of approximately 40,000 Baht, which is the amount borrowed.
• 😀 In Example 2, a loan is taken from Vayu, with two repayments due at different times: 20,291.48 Baht in 2 years and 14,859.47 Baht in 5 years, both with 8% annual interest, compounded quarterly.
• 😀 For the loan from Vayu, the future values (S) are calculated separately for each payment, and the present value (P) for each amount is computed using the same formula as in Example 1.
• 😀 The compound interest in Example 2 is calculated using quarterly compounding (k=4), meaning the interest is compounded 4 times a year.
• 😀 For the first payment of 20,291.48 Baht, the present value (P) is calculated to be approximately 20,500 Baht after applying the quarterly compounding formula.
• 😀 For the second payment of 14,859.47 Baht, the present value (P) is calculated to be approximately 10,000 Baht after applying the same formula.
• 😀 The total present value for the loan from Vayu, combining both amounts, is around 30,500 Baht, representing the total amount borrowed by the borrower.
• 😀 Both examples highlight how to apply compound interest calculations for loans with varying repayment schedules and compounding frequencies.

Q & A

What is the main topic of the transcript?

The transcript focuses on financial calculations involving loan repayment, future value, and compound interest, with specific examples of loan amounts, interest rates, and repayment periods.

What does the term 'future value' mean in the context of the transcript?

In this context, 'future value' refers to the amount of money that will need to be paid in the future, taking into account interest rates and the passage of time. It is denoted as 'S' in the formulas.

How is compound interest calculated in the examples?

Compound interest is calculated using the formula where the principal (P) is multiplied by (1 + R/k) raised to the power of -k*n, where R is the annual interest rate, k is the number of compounding periods per year, and n is the number of years.

What is the interest rate used in the examples?

The interest rate used in both examples is 8% per year, or 0.08 as a decimal.

What does 'k' represent in the compound interest formula?

In the compound interest formula, 'k' represents the number of compounding periods per year. In the first example, it is set to 1 (compounding annually), while in the second example, it is set to 4 (compounding quarterly).

What does 'n' represent in the formula, and how is it determined?

'n' represents the number of years until the future value is due. It is determined based on the repayment period provided in the script. For example, for a payment due in 2 years, n = 2.

In the first example, how much did the person borrow, and how was the amount calculated?

In the first example, the person borrowed 40,656 Baht. The amount was calculated by applying the compound interest formula to find the present value (P) based on the future value (S) of 40,656 Baht, an interest rate of 8% per year, and a 2-year repayment period.

How does the repayment period affect the calculation of the loan amount?

The repayment period affects the calculation of the loan amount because the longer the repayment period (n), the more interest is accumulated over time, resulting in a higher future value (S) that needs to be repaid. A longer repayment period leads to a lower present value (P).

What happens if the interest is compounded quarterly instead of annually?

If interest is compounded quarterly, the formula adjusts by setting 'k' to 4 (since there are 4 quarters in a year). This increases the frequency of interest application, which can result in a slightly higher total payment due to more frequent compounding.

What is the total loan repayment amount in the second example?

In the second example, the total loan repayment amount is approximately 30,000 Baht, as it combines two separate future values (one for 20,291.48 Baht due in 2 years and another for 14,859.47 Baht due in 5 years), which were each discounted to the present and added together.