Math Problem Statement

Suatu pinjaman akan dilunasi dengan anuitas bulanan. Besar anuitas Rp950.000,00 dan angsuran pertama Rp740.000,00. Jika diberlakukan suku bunga majemuk 3% per bulan, besar pinjaman tersebut adalah ........

Solution

The text in the image appears to be about calculating the principal amount of a loan that will be repaid using a monthly annuity. Here’s the extracted content:


Problem Statement: "Suatu pinjaman akan dilunasi dengan annuitas bulanan. Besar annuitas Rp950.000,00 dan angsuran pertama Rp740.000,00. Jika diberlakukan suku bunga majemuk 3% per bulan, besar pinjaman tersebut adalah ......."

Translation (if needed): "A loan will be repaid with monthly annuities. The annuity amount is Rp950,000.00 and the first payment is Rp740,000.00. If a 3% monthly compound interest is applied, the loan amount is ........."


This type of problem involves the calculation of the present value (loan amount) of an annuity.

To calculate the loan amount, the following formula is often used for the present value of an annuity under compound interest:

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

Where:

  • PP = Loan amount (present value)
  • AA = Monthly annuity (Rp950,000)
  • ii = Monthly interest rate (3% = 0.03)
  • nn = Number of months over which the loan is paid back

However, since this problem mentions that the first payment is different (Rp740,000.00), it seems that we need to account for the decreasing annuity structure, implying that the monthly payments change after the first installment. We could refine the solution after gathering more specific information like the total number of months.

Would you like me to proceed with this formula, or do you have any clarifications on the structure of the annuity (such as the number of months)?

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Math Problem Analysis

Mathematical Concepts

Annuities
Compound Interest
Present Value Calculation

Formulas

Present Value of Annuity: P = (A / i) * [1 - (1 + i)^-n]

Theorems

Present Value Theorem

Suitable Grade Level

College level, Financial Mathematics