Lecture on Bunga (Interest) in Aceh

Introduction

• Definition of Bunga (Interest): The increase in the amount of capital provided by a bank to its customers, calculated as a percentage of the customer's capital and the duration of savings. Interest can also be given by lenders.
• **Types of Interest: Bunga Tunggal (Simple Interest) and Bunga Majemuk (Compound Interest) **

Bunga Tunggal (Simple Interest)

• Definition: Interest given only on the principal amount without additional interest on previously earned interest.
• Formula for Simple Interest:
  • B = N × I × M (B = simple interest, N = number of periods, I = interest rate, M = principal amount)
• Formula for Final Amount:
  • MA = M + B (MA = final amount, M = principal amount, B = interest)
  • Can also be written as: MA = M × (1 + N × I)

Notation Explanations

• MA: Total or final amount (savings at the end of the period)
• M: Initial principal amount (savings or loan at the beginning)
• I: Interest rate
• N: Number of periods
• B: Interest at the end of the Nth period
• Period Consistency: Periods must be consistent. If the rate is per year, then periods must also be per year.

Example Problems

1. Example 1:

   • Problem: Agus deposits 1 million with a simple interest rate of 5% per year. Calculate the interest at the end of the third year.
   • Solution: Principal M = 1 million, I = 5% (0.05 in decimals), N = 3 years.
     • B = 3 × 0.05 × 1,000,000 = 150,000 IDR interest
   • Final amount: MA = 1,000,000 + 150,000 = 1,150,000 IDR

2. Example 2:

   • Problem: A father deposits 5 million with an interest rate of 18% per year. Calculate the total amount at the end of 5 months.
   • Solution: Convert annual interest rate to monthly: 18%/12 = 1.5% per month (0.015 in decimals).
     • B = 5 × 0.015 × 5,000,000 = 375,000 IDR interest
   • Final amount: MA = 5,000,000 + 375,000 = 5,375,000 IDR

Bunga Majemuk (Compound Interest)

• Definition: Interest given not only on the principal but also on previously earned interest.
• Formula for Compound Interest:
  • BM = M × [(1 + I)^N - 1]
• Formula for Final Amount:
  • MA = M × (1 + I)^N

Notation Explanations

• MA: Total or final amount (savings at the end of the period)
• M: Initial principal amount (savings or loan at the beginning)
• I: Interest rate
• N: Number of periods
• B: Interest at the end of the Nth period
• Period Consistency: Periods must be consistent. If the rate is per year, then periods must also be per year.

Example Problems

1. Example 3:

   • Problem: Ifani saves 1 million at a compound interest rate of 10% per year. Calculate the interest at the end of the third year.
   • Solution: Principal M = 1 million, I = 10% (0.1 in decimals), N = 3 years.
     • BM = 1,000,000 × [(1 + 0.1)^3 - 1] = 1,000,000 × [1.331 - 1] = 331,000 IDR interest
   • Final amount: MA = 1,000,000 × 1.331 = 1,331,000 IDR

2. Example 4:

   • Problem: Ifani saves 1 million at a compound interest rate of 10% per year. Calculate the total amount at the end of the third year.
   • Solution: Principal M = 1 million, I = 10% (0.1 in decimals), N = 3 years.
     • MA = 1,000,000 × (1 + 0.1)^3 = 1,000,000 × 1.331 = 1,331,000 IDR

Conclusion

• Review: Reviewed the definitions, formulas, and example problems for both simple and compound interests.
• Next Steps: Stay consistent with period calculations and proper conversion between percentages and decimals.