The problem involves calculating the remaining balance on a loan after certain payments have been made with interest applied annually. Let's break it down step by step:

Given Data:

• Loan Amount (Principal): Rp 8,900,000
• Interest Rate: 5.25% annually
• Payment at the end of the 1st year: Rp 2,000,000
• Payment at the end of the 2nd year: Rp 3,000,000
• Goal: Find the remaining amount to be paid at the end of the 3rd year to fully repay the loan.

Solution:

1. Calculate the balance after the 1st year:

The interest is compounded yearly. At the end of the first year, the amount owed is calculated as: $\text{Amount Owed} = \text{Principal} \times (1 + \text{Interest Rate}) - \text{Payment}$

$\text{Amount Owed after 1st year} = 8,900,000 \times (1 + 0.0525) - 2,000,000$ $\text{Amount Owed after 1st year} = 8,900,000 \times 1.0525 - 2,000,000$ $\text{Amount Owed after 1st year} = 9,366,250 - 2,000,000 = 7,366,250$

2. Calculate the balance after the 2nd year:

At the end of the second year, the remaining balance accrues interest, and another payment is made: $\text{Amount Owed after 2nd year} = \text{Balance from 1st year} \times (1 + \text{Interest Rate}) - \text{Payment}$

$\text{Amount Owed after 2nd year} = 7,366,250 \times 1.0525 - 3,000,000$ $\text{Amount Owed after 2nd year} = 7,752,406.25 - 3,000,000 = 4,752,406.25$

3. Calculate the payment required at the end of the 3rd year:

At the end of the third year, the remaining balance accrues interest again. To fully repay the loan, the amount to be paid is: $\text{Payment after 3rd year} = \text{Balance from 2nd year} \times (1 + \text{Interest Rate})$

$\text{Payment after 3rd year} = 4,752,406.25 \times 1.0525$ $\text{Payment after 3rd year} = 5,001,656.57$

Final Answer:

The amount that needs to be paid at the end of the third year is Rp 5,001,656.57.

Would you like a detailed explanation of any specific part of the calculation? Here are some related questions to expand upon this:

1. How is compound interest different from simple interest?
2. Can you explain how loan repayments are structured in real-world scenarios?
3. How would the result change if payments were made at the beginning of the year instead?
4. How does the interest rate affect the total repayment amount?
5. What tools can be used to quickly calculate loan repayments?

Tip: Always confirm the payment schedule and interest compounding method when dealing with financial calculations to ensure accuracy.