Anuitas || Matematika Wajib Kelas XI

Summary

This video script explains the concept of annuities, including their definition, formulas, and practical applications. An annuity is a fixed payment made at regular intervals, and the script covers two primary formulas used to calculate annuities. It then explores various related concepts such as insurance, loan repayments, interest rates, and the process of calculating the remaining loan balance. Through example problems, the script demonstrates how to apply the formulas and create an amortization table for loan repayments. It also details how to calculate interest and principal portions of the payments for each period, making the topic clear and accessible.

Takeaways

• 😀 Annuities involve fixed, regular payments or receipts over a set period of time, with the amount remaining constant across periods.
• 😀 There are two main formulas to calculate annuities depending on the available information: one for known installments and interest, and another for known loan amounts and interest rates.
• 😀 The first formula for annuities is: Annuity = A_n + B_n. The second formula is: Annuity = M × [1 / (1 - (1 + i)^{-n})].
• 😀 The choice of formula depends on what is known in the problem: either installments and interest (use the first formula) or loan amounts and interest rates (use the second formula).
• 😀 When calculating installments, there are two methods: subtracting the interest from the annuity (KM = A - B), or using a compounded growth formula (KM = A × (1 + i)^n).
• 😀 Interest can be calculated using two formulas: either subtracting the installment from the annuity (B = A - KM), or multiplying the loan amount by the interest rate (B = M × i).
• 😀 To calculate the remaining balance of the loan, subtract the installments from the loan balance for each period (S_M = M - KM).
• 😀 An example is provided where a loan of 5 million Rupiah is paid in 5 periods with a 2% monthly interest rate. The annuity is calculated using the second formula to be 1,060,792 Rupiah per period.
• 😀 A table for loan repayment is created, showing the decreasing loan balance, interest, and installment for each period. The interest is calculated based on the remaining loan amount.
• 😀 In the second example, a loan of 15 million Rupiah with a monthly annuity of 800,000 Rupiah and a 1.2% interest rate is used to calculate the first interest and installment values.

Q & A

What is the definition of an annuity?

An annuity is a series of regular payments or receipts of equal amounts made at specified intervals over a certain period of time.

What are the two formulas for calculating annuities mentioned in the script?

The two formulas for calculating annuities are: 1) Annuity = A * (1 - (1 + i)^(-n)) / i, and 2) Annuity = A + B, where A is the principal or loan amount, B is the interest, i is the interest rate per period, and n is the number of periods.

How do you determine which annuity formula to use?

The choice of formula depends on the given information in the problem. If the problem provides the loan amount and interest rate, the second formula is used. If it provides the loan repayment and interest, the first formula is used.

What is the difference between the terms A and B in the annuity formulas?

In the formulas, A refers to the loan or principal amount, while B refers to the interest. The two are combined in the second formula to calculate the annuity.

How do you calculate the installment (angsurans) from the annuity formula?

To calculate the installment, you can use the formula: Installment = Annuity - Interest, where Annuity is the total payment and Interest is calculated by multiplying the loan balance by the interest rate for that period.

What is the formula for calculating the interest in an annuity loan?

The interest for each period is calculated using the formula: Interest = Loan Balance * Interest Rate, where the loan balance is the remaining principal at the start of each period.

How do you calculate the remaining balance of the loan (sisa pinjaman) after each installment?

The remaining balance is calculated by subtracting the installment payment from the current loan balance. This remaining balance becomes the loan balance for the next period.

What is the purpose of the annuity table (tabel rencana angsuran) in the example?

The annuity table is used to organize and track the loan's progress. It lists each period's loan balance, the fixed annuity payment, the interest, the installment, and the remaining loan balance after each payment.

In the second example, what was the first month's interest on a 15 million loan at 1.2% monthly interest?

The first month's interest was 180,000, calculated as 15,000,000 * 0.012 (1.2% monthly interest).

What happens to the remaining loan balance after the final payment in an annuity system?

After the final payment in an annuity system, the remaining loan balance should be zero, meaning the loan has been fully repaid by the end of the term.