ANUITAS

Summary

This educational video explains how to calculate various aspects of loan repayments using the annuity system, covering both annual and monthly payment scenarios. It demonstrates how to compute installment payments, interest amounts, and principal repayments through several examples. The video walks through calculating the total annuity, first installment, and interest payments for different cases, including a loan with a fixed monthly annuity and varying interest rates. The content provides a clear understanding of using annuity formulas, geometric progression, and financial principles to solve real-world loan problems.

Takeaways

• 😀 Annuities are used to repay loans with fixed, periodic payments (e.g., annual or monthly).
• 😀 In the first example, the annual payment (annuity) is calculated by adding the installment and interest payments.
• 😀 For the first question, the total annual payment is Rp 1,350,000, which is the sum of the fifth installment (Rp 250,000) and the fifth interest (Rp 1,100,000).
• 😀 The second problem involves monthly payments, where the annuity is Rp 600,000. The first installment is calculated by subtracting the first interest (Rp 420,000) from the annuity.
• 😀 The first installment in the second example is Rp 180,000 (Rp 600,000 - Rp 420,000).
• 😀 The 10th interest is determined by subtracting the 10th installment (Rp 250,000) from the total annuity (Rp 600,000), yielding Rp 350,000.
• 😀 The third problem involves a loan of Rp 20 million to be repaid with a fixed monthly annuity of Rp 500,000 and an interest rate of 1.5% per month.
• 😀 The first interest payment in the third example is calculated by multiplying the loan amount (Rp 20 million) by the monthly interest rate (1.5%), yielding Rp 300,000.
• 😀 The first installment in the third example is Rp 200,000 (Rp 500,000 - Rp 300,000).
• 😀 For the 10th installment in the third example, a geometric sequence formula is used, where the first installment (Rp 200,000) is multiplied by (1 + 0.015)^9, yielding Rp 228,678.
• 😀 The 10th interest in the third example is calculated by subtracting the 10th installment (Rp 228,678) from the total annuity (Rp 500,000), resulting in Rp 271,322.

Q & A

What is the first step in calculating the annuity for a loan repayment?

The first step in calculating the annuity for a loan repayment is to determine the amount of the fifth installment and the fifth interest, as these values are used to derive the total annuity.

How is the total annuity calculated in the first example?

In the first example, the total annuity is calculated by adding the fifth installment (Rp250,000) and the fifth interest (Rp1,100,000), resulting in a total annuity of Rp1,350,000.

What is the relationship between the annuity, the installment, and the interest in loan repayments?

The annuity is the sum of the installment and the interest. For each period, the total payment includes both the principal installment and the interest due for that period.

How do you calculate the first installment if the total annuity is known?

To calculate the first installment, subtract the first interest from the total annuity. For example, with a total annuity of Rp600,000 and the first interest of Rp420,000, the first installment is Rp600,000 - Rp420,000 = Rp180,000.

What is the method to calculate the interest for the 10th installment in the second example?

The interest for the 10th installment is calculated by subtracting the 10th installment from the total annuity. For example, the annuity is Rp600,000, and the 10th installment is Rp250,000, so the interest is Rp600,000 - Rp250,000 = Rp350,000.

How do you calculate the first installment in the second example?

To calculate the first installment in the second example, subtract the first interest (Rp420,000) from the total annuity (Rp600,000), which gives the first installment as Rp600,000 - Rp420,000 = Rp180,000.

How is the 10th installment calculated using the geometric sequence formula?

The 10th installment is calculated using the formula for a geometric sequence, where the ratio is 1 + the monthly interest rate. In this case, the formula is A1 * (1 + 0.015)^(10-1), and multiplying by the first installment of Rp200,000 gives the 10th installment as Rp228,678.

How is the first interest calculated in the third example with a loan of Rp20 million?

The first interest is calculated by multiplying the initial loan amount (Rp20,000,000) by the monthly interest rate (0.015). This gives Rp20,000,000 * 0.015 = Rp300,000.

What is the total amount of the 10th installment in the third example?

The total amount of the 10th installment in the third example is calculated using the formula for a geometric sequence. The result for the 10th installment is Rp228,678.

What is the significance of the 10th interest in the third example?

The 10th interest is calculated by subtracting the 10th installment from the total annuity. In the third example, the interest is calculated as Rp500,000 (annuity) - Rp228,678 (10th installment), resulting in an interest of Rp271,322.