Applikasi Deret Geometri - Ani menabung di bank sebesar 10 juta dengan bunga majemuk 4% per tahun. T

Introduction

In this tutorial, we will explore the concept of geometric series and how to calculate the future value of savings using compound interest. We will specifically look at a scenario where Ani saves 10 million with a compound interest rate of 4% per year. Understanding these concepts is essential for making informed financial decisions and grasping the principles of geometric sequences.

Step 1: Understanding Geometric Series

• A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

• The general formula for finding the n-th term of a geometric series is:

  [ a_n = a_1 \times r^{(n-1)} ]

  where:

  • (a_n) is the n-th term
  • (a_1) is the first term
  • (r) is the common ratio
  • (n) is the term number

Step 2: Calculating the Future Value of Savings

To calculate how much Ani will have after 5 years, we will use the compound interest formula:

[ A = P(1 + r)^n ]

Where:

• (A) is the amount of money accumulated after n years, including interest.
• (P) is the principal amount (the initial amount of money).
• (r) is the annual interest rate (decimal).
• (n) is the number of years the money is invested or borrowed.

Practical Steps to Calculate the Future Value

1. Identify the Variables:

   • Principal amount (P = 10,000,000) (10 million)
   • Annual interest rate (r = 0.04) (4% as a decimal)
   • Number of years (n = 5)

2. Plug the Values into the Formula: [ A = 10,000,000 (1 + 0.04)^5 ]

3. Calculate the Amount:

   • First, calculate (1 + 0.04 = 1.04).
   • Next, raise (1.04) to the power of (5): [ 1.04^5 \approx 1.21665 ]
   • Now multiply by the principal: [ A \approx 10,000,000 \times 1.21665 \approx 12,166,500 ]

Step 3: Conclusion of the Calculation

After 5 years, Ani's savings will grow to approximately 12,166,500.

Key Takeaways

• Geometric series and formulas are crucial for understanding compound interest.
• Regularly saving and investing can significantly increase your financial health over time.
• Always ensure to understand the terms in financial calculations to make informed decisions.

Conclusion

In this tutorial, we learned how to analyze a geometric series and apply it to a real-world savings problem involving compound interest. By understanding these concepts, you can better plan your financial future. Consider applying these calculations to your own savings goals or investments.