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.