Math Problem Statement

Pinjaman sebesar Rp 25.000.000,00 dibiayai dengan annuitas bulanan selama 2 tahun 6 bulan dengan suku bunga 3,25% per bulan. Angsuran pertama yang harus diberikan adalah?

Solution

The problem you provided refers to a loan of Rp 25,000,000 being financed with monthly annuities for 2 years and 6 months, with an interest rate of 3.25% per month. It asks for the amount of the first installment (Angsuran pertama).

To calculate the monthly annuity payment, we can use the formula for the annuity payment for a loan:

A=P×(i×(1+i)n(1+i)n1)A = P \times \left( \frac{i \times (1 + i)^n}{(1 + i)^n - 1} \right)

Where:

  • AA is the annuity (monthly installment)
  • PP is the principal (Rp 25,000,000)
  • ii is the monthly interest rate (3.25% = 0.0325)
  • nn is the number of periods (30 months for 2 years and 6 months)

Let me calculate the exact value.The first monthly installment (annuity payment) for the loan is approximately Rp 1,317,042.92.

It appears that none of the options in the provided image match this value exactly. The possible discrepancies might arise from rounding or different interpretations of interest compounding.

Would you like further clarification or details on how this result was obtained?

Here are some related questions to consider:

  1. How does the interest rate affect the monthly installment?
  2. What happens if the loan duration changes to 3 years instead of 2.5 years?
  3. How is the total interest paid over the entire loan period calculated?
  4. What is the difference between simple and compound interest in loan payments?
  5. How would an earlier repayment affect the total cost of the loan?

Tip: Always check if the loan interest is compounded monthly or annually, as this can significantly impact the payment amount.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Annuity
Loan Amortization
Interest Rate Calculation

Formulas

A = P * (i * (1 + i)^n) / ((1 + i)^n - 1)

Theorems

Annuity formula

Suitable Grade Level

Grades 11-12