Calculation Tricks for Fast Results

Introduction

• Understanding important tricks can significantly speed up calculations.
• Focus: compound interest, future value (annuity), and present value (annuity).
• Aimed at improving exam speed and accuracy without a calculator.

Trick 1: Compound Interest

• Conventional knowledge involves using the formula for compound interest.

• Fast Method: Adding 10% thrice without formula.

  Formula: [ A = P \left(1 + \frac{R}{100}\right)^N ]

  • Example 1: Principal (P) = 1000, Rate (R) = 10%, Times (N) = 3
    • Manually adding:
      • First increment: 1000 + 10% = 1100
      • Second increment: 1100 + 10% = 1210
      • Third increment: 1210 + 10% = 1331
    • Compound Interest: 1331 - 1000 = 331
  • Example 2: Principal (P) = 500, Rate (R) = 5%, Times (N) = 3
    • Calculate similarly using percentages on calculator.

Trick 2: Future Value of Annuity

• Formula: [ FV_{annuity} = A * \left( \frac{(1 + i)^N - 1}{i} \right) ]

  • **Definitions:
    • A = Annuity amount
    • i = Rate of interest (as a decimal)
    • N = Number of periods
  • Example: A = 100, i = 0.1 (10%), N = 10
    • Calculation steps on a calculator:
      • ( (1 + i)^N
        • Calculate 1.1^10 using repeated multiplication until step value reaches 11.
        • Subtract 1 from this value.
        • Divide by 0.1.
        • Multiply final result by 100.
    • Result: 1593.74 (approx.)
  • Example 2: A = 500, i = 0.05 (5%), N = 20
    • Perform similar steps on a calculator for exact value.

Trick 3: Present Value of Annuity

• Formula: [ PV_{annuity} = A * \left( \frac{1 - (1+i)^{-N}}{i} \right) ]

  • **Definitions:
    • A = Annuity amount
    • i = Rate of interest (as a decimal)
    • N = Number of periods
  • Example: A = 100, i = 0.1 (10%), N = 10
    • Calculation steps on a calculator:
      • Solve (1 + 0.1)^10 for a step value reaching 11.
      • Subtract 1 from this value and finally divide by 0.1.
      • Multiply by 100 for result.
    • Result: 614.457 (approx.)
  • Example 2: A = 500, i = 0.05 (5%), N = 20
    • Similar steps on calculator for exact value.

Conclusion

• Tricks such as these can save time during examinations.
• Practice is key to mastering these methods.
• For more tricks on different chapters, feel free to ask for specific calculations.