https://file.aiquickdraw.com/mathbot/file/1726124578407qhcobzr0.jpg

Let's work through the problems from the image you provided.

### Problem 1:
**Calculate the final amount of capital from Rp. 5,000,000 borrowed for 1 year with an interest rate of 1% per month.**

This involves simple interest, calculated as:

\[
A = P \times (1 + r \times t)
\]
Where:
- \( P \) is the principal amount (Rp. 5,000,000),
- \( r \) is the interest rate per month (1% or 0.01),
- \( t \) is the time in months (12 months for 1 year).

Let's calculate that in the next step.

### Problem 2:
**Rp. 20,000,000 is borrowed with a 2% annual interest rate, compounded annually. What is the capital at the beginning of period 3?**

This involves compound interest:
\[
A = P \times (1 + r)^t
\]
Where:
- \( P \) is Rp. 20,000,000,
- \( r \) is the annual interest rate (2% or 0.02),
- \( t \) is the number of years (3 years).

We'll calculate the amount at the start of the 3rd period.

### Problem 3:
**A loan of Rp. 10,000,000 is repaid using an annuity with a yearly payment of Rp. 2,000,000. The interest rate is 5% per year. Find the remaining loan balance at the end of year 3.**

This is solved using the annuity formula. Given the 5% annual interest and 3-year time frame, we will calculate the remaining balance after 3 years.

### Final Table Question:
The last part of the problem involves interpreting the given amortization table and calculating the remaining loan balance at the end of year 3 based on an interest rate of 3.5%, using the given annuity of Rp. 550,100.

Let me begin by calculating the relevant parts for you.### Results:
1. **Final amount for the loan of Rp. 5,000,000 with 1% monthly interest over 1 year:**
   \[
   A = Rp. 5,600,000
   \]
   
2. **The capital at the beginning of the 3rd period (after 2 years) for a loan of Rp. 20,000,000 with 2% annual compound interest:**
   \[
   A = Rp. 20,808,000
   \]

Next, let's calculate the remaining balance after year 3 in the annuity loan case. I'll work on that now.For the **annuity loan problem**, we need to calculate the remaining balance after year 3. The loan is Rp. 10,000,000, with annual payments of Rp. 2,000,000 and a 5% annual interest rate. 

The remaining balance can be calculated using the amortization formula for annuities:

\[
B_t = P \times (1 + r)^t - A \times \frac{(1 + r)^t - 1}{r}
\]
Where:
- \( P \) is the initial loan (Rp. 10,000,000),
- \( r \) is the interest rate per year (5% or 0.05),
- \( t \) is the time (3 years),
- \( A \) is the annuity payment (Rp. 2,000,000).

I'll now calculate the remaining balance at the end of year 3.It seems like I can’t do more advanced data analysis right now. Please try again later. 

Would you like to review the steps involved, or perhaps we can tackle any of the other problems in detail?

### Here are some follow-up questions to expand on the topics we've covered:
1. How do you distinguish between simple and compound interest formulas?
2. Why does compound interest result in a higher final amount than simple interest for the same rate and period?
3. What effect does increasing the interest rate have on annuity calculations?
4. How is an amortization schedule constructed for loan repayments?
5. Can you explain the difference between an annuity and a standard loan repayment?

### Tip: When calculating loan amortization, always make sure to check how interest is applied (annually, monthly, etc.) to avoid under- or over-estimating the loan balance.

Calculate the final capital of Rp. 5,000,000 borrowed for 1 year at an interest rate of 1% per month. Also, calculate the capital at the beginning of period 3 for a Rp. 20,000,000 loan with a 2% annual interest rate compounded annually. Finally, for a Rp. 10,000,000 loan with an annual annuity of Rp. 2,000,000 and a 5% interest rate, determine the remaining balance at the end of year 3.

Solve various financial problems involving loan interest and annuities, including calculating the final capital of a Rp. 5,000,000 loan, the capital after 3 periods for Rp. 20,000,000 with 2% compound interest, and finding the remaining balance for a Rp. 10,000,000 loan with annuities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation