The image you uploaded contains compound interest problems. Let's go through the problems one by one and solve them. The compound interest formula we'll use is:

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

Where:

• $A$ = the amount of money accumulated after n years, including interest.
• $P$ = the principal (initial investment).
• $r$ = annual interest rate (in decimal form).
• $n$ = number of times the interest is compounded per year.
• $t$ = the time the money is invested or borrowed for, in years.

Let's break down the questions.

Question 1:

Principal $P = 2,500,000$ IDR, Annual Interest $r = 12\%$, Time $t = 8$ years, Compounded annually.

• Here, $n = 1$.

$A = 2,500,000 \left(1 + \frac{0.12}{1}\right)^{1 \times 8}$

Let's compute the final amount.

Question 2:

Principal $P = 4,800,000$ IDR, Quarterly Compounded Interest $r = 6\%$, Time $t = 3.5$ years.

• Quarterly means $n = 4$.

$A = 4,800,000 \left(1 + \frac{0.06}{4}\right)^{4 \times 3.5}$

Question 3:

Principal $P = 4,500,000$ IDR, Quarterly Compounded Interest $r = 4\%$, Time $t = 5$ years and 4 months.

• First, convert 5 years 4 months into years: $5 + \frac{4}{12} = 5.3333$ years.
• Quarterly compounding, so $n = 4$.

$A = 4,500,000 \left(1 + \frac{0.04}{4}\right)^{4 \times 5.3333}$

Question 4:

Principal $P = 5,000,000$ IDR, Annual Compounded Interest $r = 10\%$, Time $t = 6$ years.

• Here, $n = 1$.

$A = 5,000,000 \left(1 + \frac{0.10}{1}\right)^{1 \times 6}$

Question 5:

Principal $P = 100,000$ IDR, Annual Interest $r = 5\%$, Time $t = 5$ years, Compounded annually.

• Here, $n = 1$.

$A = 100,000 \left(1 + \frac{0.05}{1}\right)^{1 \times 5}$

I'll now compute the solutions for each question.Here are the solutions to the compound interest problems:

1. Question 1: The final amount after 8 years with an initial capital of Rp 2,500,000 and 12% annual interest is Rp 6,189,907.94.

2. Question 2: The final amount after 3.5 years with an initial capital of Rp 4,800,000 and 6% quarterly compounded interest is Rp 5,912,427.51.

3. Question 3: The final amount after 5 years and 4 months with an initial capital of Rp 4,500,000 and 4% quarterly compounded interest is Rp 5,564,188.33.

4. Question 4: The final amount after 6 years with an initial capital of Rp 5,000,000 and 10% annual compounded interest is Rp 8,857,805.00.

5. Question 5: The final amount after 5 years with an initial capital of Rp 100,000 and 5% annual interest is Rp 127,628.16.

Do you need further details or clarifications?

Here are some related questions for practice:

1. How would the result change if the interest in question 1 was compounded monthly?
2. What would the final amount be for question 2 if the interest rate were 8% instead?
3. How does quarterly compounding affect the result compared to annual compounding in question 3?
4. In question 4, what happens if the time is reduced to 4 years but the interest rate remains the same?
5. How would you calculate the effective interest rate in question 5?

Tip: More frequent compounding generally leads to higher returns due to more frequent application of interest on the principal.