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9.	Jeremy ingin membeli rumah secara KPR, tetapi belum memutuskan bank yang akan digunakan. Harga rumah tersebut adalah Rp350.000.000,00 dan Jeremy membayar uang muka sebesar Rp70.000.000,00. Jika Jeremy memilih Bank Negara Indoensia yang menawarkan anuitas bulanan selama tiga tahun, pasangkan pernyataan berikut dengan jawaban yang benar.

Pernyataan							Jawaban
Anutias per bulan yang harus dibayarkan Jeremy 		Rp8.686.700,00
Angsuran awal yang harus dibayarkan Jeremy		Rp7.006.700,00
angsuran ketiga yang harus dibayarkan Jeremy		Rp7.090.800,00
								Rp7.892.000,00
jawablah menggunakan cara yang benar dan  detail

Let's walk through Jeremy's mortgage (KPR) calculation in detail using the provided information:

### Key information:
- **Bank**: Bank Negara Indonesia (BNI)
- **Home price**: Rp 350,000,000
- **Down payment**: Rp 70,000,000
- **Loan principal**: Rp 350,000,000 - Rp 70,000,000 = Rp 280,000,000
- **Loan term**: 3 years (36 months)
- **Interest rate (KPR)**: 7.25% annually, as per the table for Bank Negara Indonesia

### Formula used for calculating the monthly annuity (installment) payment:
The formula for calculating the monthly payment of a loan with fixed installments is:

\[
A = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]

Where:
- \(A\) = monthly installment (to be determined)
- \(P\) = loan principal (Rp 280,000,000)
- \(r\) = monthly interest rate (annual rate divided by 12)
- \(n\) = total number of installments (36 months for a 3-year loan)

### Step 1: Calculate the monthly interest rate
Since the annual interest rate is 7.25%, we divide this by 12 to get the monthly rate.

\[
r = \frac{7.25\%}{12} = \frac{0.0725}{12} = 0.00604
\]

### Step 2: Total number of months
For a 3-year loan, the number of months \(n\) is 36.

### Step 3: Calculate the monthly payment
Substitute the values into the formula:

\[
A = 280,000,000 \times \frac{0.00604(1 + 0.00604)^{36}}{(1 + 0.00604)^{36} - 1}
\]

Using a calculator:

\[
A \approx 280,000,000 \times \frac{0.00604 \times 1.24313}{0.24313}
\]
\[
A \approx 280,000,000 \times 0.03087
\]
\[
A \approx 8,643,600
\]

So, Jeremy's monthly installment is approximately **Rp 8,643,600**.

### Comparing to the provided answers:
- **Annuity per month** (which Jeremy will pay each month): Rp **8.686.700**, which is very close to the calculation.
- **First installment (angsuran awal)** and the **third installment** can differ slightly based on the bank’s method of applying interest, typically amortized in a way that slightly decreases the principal owed over time.

Would you like to dive into the calculation of specific early installments or explore how amortization affects the repayment schedule in more detail?

### 5 Further Related Questions:
1. How does the down payment affect the total interest Jeremy will pay over 3 years?
2. What would the total interest paid be if Jeremy took a longer-term loan (e.g., 10 years)?
3. How does the monthly payment change if the interest rate increases by 0.5%?
4. What is the total amount Jeremy will have paid by the end of the loan period?
5. How does an annuity-based loan compare to an equal principal loan?

### Tip:
When considering a mortgage, it's important to look beyond the monthly payment and evaluate the total cost of the loan over its term, especially the interest paid!

Jeremy ingin membeli rumah secara KPR, tetapi belum memutuskan bank yang akan digunakan. Harga rumah tersebut adalah Rp350.000.000,00 dan Jeremy membayar uang muka sebesar Rp70.000.000,00. Jika Jeremy memilih Bank Negara Indonesia yang menawarkan anuitas bulanan selama tiga tahun, pasangkan pernyataan berikut dengan jawaban yang benar.

Learn how to calculate the monthly annuity payments for a KPR (Kredit Pemilikan Rumah) loan using Bank Negara Indonesia's interest rate. The problem involves a house price of Rp350,000,000 with a down payment of Rp70,000,000 and an annual interest rate of 7.25%. Detailed step-by-step solution included, ideal for students in Grades 10-12.

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