The problem states that a loan of Rp10,000,000.00 is being repaid through monthly annuities at an interest rate of 3.5% per month for 3 years (36 months). It asks to determine the remaining loan balance after 25 months of payments.

Let's break it down:

1. Loan amount (P): Rp 10,000,000
2. Interest rate per month (i): 3.5% or 0.035
3. Loan period (n): 36 months
4. Time of calculation (after 25 months): 25 months

To calculate the remaining loan balance after 25 months, we first need to calculate the monthly annuity payment (A). Then we use the remaining balance formula to find how much is still owed.

Step 1: Calculate the Monthly Payment (A)

The formula for the monthly payment on an amortizing loan is: $A = \frac{P \cdot i}{1 - (1 + i)^{-n}}$ Where:

• $P = 10,000,000$
• $i = 0.035$
• $n = 36$

Step 2: Calculate the Remaining Balance after 25 months

The remaining loan balance after $k$ months of payments is calculated by: $S_k = P \cdot (1 + i)^k - \frac{A \cdot [(1 + i)^k - 1]}{i}$ Where $S_k$ is the balance after $k = 25$ months.

Let me calculate this for you.The monthly payment (annuity) is approximately Rp 492,841.63.

After 25 months of making these payments, the remaining loan balance is approximately Rp 4,436,339.07.

Would you like any more details or have any questions? Here are some related questions to deepen your understanding:

1. How is the annuity formula derived for loan payments?
2. What happens if the interest rate changes during the repayment period?
3. How does paying more than the required monthly payment affect the loan balance?
4. Can this method be applied to loans with varying interest rates?
5. What is the impact of making an early lump-sum payment on the remaining loan balance?

Tip: Understanding how loan amortization works helps you see how much interest versus principal you're paying each month. This can be useful for planning to reduce debt faster!