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Let's solve these financial mathematics problems one by one:

### 1. **Seorang investor mendapatkan bunga majemuk 4% per tahun dari modal sebesar Rp10.000.000. Berapa nilai investasi setelah 2 tahun?**

This is a compound interest problem. The formula for compound interest is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- \( A \) = Final amount (nilai investasi akhir)
- \( P \) = Principal (modal awal) = Rp10.000.000
- \( r \) = Annual interest rate (bunga per tahun) = 4% = 0.04
- \( t \) = Time in years = 2
- \( n \) = Compounding frequency per year. Since the problem doesn't specify, we assume it's annually, so \( n = 1 \).

Plugging in the values:

\[
A = 10,000,000 \left(1 + \frac{0.04}{1}\right)^{1 \times 2}
\]

\[
A = 10,000,000 \left(1.04\right)^2 = 10,000,000 \times 1.0816 = 10,816,000
\]

So, the value of the investment after 2 years is **Rp10.816.000**. The closest answer is **Rp10.816.000**.

---

### 2. **Jika seseorang menyetor Rp1.000.000 setiap akhir bulan selama 3 tahun dengan bunga 6% per tahun yang dibayar bulanan, maka nilai akhir dari anuitas tersebut adalah?**

This is an ordinary annuity problem where monthly payments are made with interest. The formula for the future value of an ordinary annuity is:

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

Where:
- \( A \) = Future value of the annuity
- \( P \) = Monthly payment = Rp1.000.000
- \( r \) = Annual interest rate = 6% = 0.06
- \( n \) = Number of compounding periods per year = 12 (monthly payments)
- \( t \) = Time in years = 3

Plugging in the values:

\[
A = 1,000,000 \times \frac{(1 + 0.06/12)^{12 \times 3} - 1}{0.06/12}
\]

\[
A = 1,000,000 \times \frac{(1.005)^{36} - 1}{0.005}
\]

Calculating the future value:

\[
A = 1,000,000 \times \frac{1.196682 - 1}{0.005} = 1,000,000 \times 39.3364 = 39,336,400
\]

So, the final value of the annuity is approximately **Rp39.336.400**, closest to **Rp39.415.940**.

---

### 3. **Seorang investor menanamkan modal sebesar Rp10.000.000 dengan bunga tunggal 8% per tahun. Berapa besar bunga yang diperoleh setelah 2 tahun?**

This is a simple interest problem. The formula for simple interest is:

\[
I = P \times r \times t
\]

Where:
- \( I \) = Interest earned (bunga yang diperoleh)
- \( P \) = Principal (modal awal) = Rp10.000.000
- \( r \) = Annual interest rate = 8% = 0.08
- \( t \) = Time in years = 2

Plugging in the values:

\[
I = 10,000,000 \times 0.08 \times 2 = 10,000,000 \times 0.16 = 1,600,000
\]

So, the interest earned after 2 years is **Rp1.600.000**. The correct answer is **Rp1.600.000**.

---

Do you need further details or explanations for any of these questions? 

Here are 5 related questions to explore these topics further:
1. How does the frequency of compounding affect the final investment value?
2. What would be the value of the investment in the first question if the interest were compounded monthly?
3. How can the future value of an annuity differ if payments are made at the beginning of the month?
4. How is compound interest different from simple interest in long-term investments?
5. How would the final amount change in question 1 if the interest rate increased to 5%?

**Tip:** Always confirm whether interest is compounded monthly, annually, or quarterly, as it can significantly change the final amount.

Seorang investor mendapatkan bunga majemuk 4% per tahun dari modal sebesar Rp10.000.000. Berapa nilai investasi setelah 2 tahun?

Learn how to calculate compound interest, annuities, and simple interest with these three financial math problems. The problems cover investment returns, monthly payments, and interest earnings in a practical context.

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