Math Problem Statement
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:
Where:
- = Loan amount (present value)
- = Monthly annuity (Rp950,000)
- = Monthly interest rate (3% = 0.03)
- = 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)?
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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
Related Recommendation
Loan Annuity Payment Calculation for Rp 600,000 with Rp 415,000 Payment at Installment 5
Anuitas Pembayaran: Rp 1.400.000 dengan Bunga 14%
Calculate Monthly Annuity for Loan Repayment with 4% Interest Rate
Annuity Loan Repayment Calculation with 4% Interest Rate Over 25 Months
Annuity Calculation for Loan Repayment Schedule with 6% Interest