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Investment Return Calculation Guide

To accurately calculate investment returns, both the invested amount and the applicable interest rate must be known. For this example, we assume:

• Investment Amount: X
• Interest Rate: 50% return over a 6-month period

Understanding the Calculation

1. Annual Interest Rate

Since the investment yields a 50% return over 6 months, the implied annual interest rate is 100% (i.e., 50\% \times 2).

2. Daily Interest Rate

To determine returns over shorter periods, we calculate the effective daily interest rate using the compound interest formula:

\text{Daily Interest Rate} = (1 + r)^{1/n} - 1

Where:

• r = 1 (representing a 100% annual rate)
• n = 365 (number of days in a year)

Return Calculations Over Different timeframes Using the daily compounding approach, we derive approximate returns for different durations:

Time Period.                Formula.                          Return.

24 hours.      X \times (1 + 1)^{1/365} - X.      ≈ 0.27% of X

7 Days.         X \times (1 + 1)^{7/365} - X.      ≈ 1.9% of X

14 Days.       X \times (1 + 1)^{14/365} - X.     ≈ 3.8% of X

30 Days.       X \times (1 + 1)^{30/365} - X.     ≈ 7.9% of X

3 months.     X \times (1 + 1)^{90/365} - X.     ≈ 24% of X

6 months.     X \times 0.5 (given directly).          = 50% of X

12 months.   X \times 1 (based on annual rate).  = 100% of X

Summary

These calculations provide a clear view of how investment returns scale over time when compounding daily, based on an effective annual interest rate of 100%. The formula applied ensures accurate compounding effects over various durations.