Rate of Return on Investment (ROI) Calculator

What is ROI?

Rate of Return on Investment (ROI) is a measure used to evaluate the efficiency or profitability of an investment. It compares the gain or loss from an investment relative to its cost.

Formula for Calculating ROI

The formula to calculate the future value of your investment is:

\[FV = PV + \sum_{i=1}^{n} (C \times (1 + r)^i)\]

Where:

• \(FV\) = Future Value (total savings)
• \(PV\) = Present Value (initial investment)
• \(C\) = Return Amount
• \(r\) = Rate of Return
• \(n\) = Number of Years

Step-by-Step Calculation

1. Determine the initial investment (\(PV\)): \[PV = \$10,000\]
2. Calculate the return amount (\(C\)): \[C = \$5,000\]
3. Apply the rate of return (\(r\)) and number of years (\(n\)): \[r = 7\%\] \[n = 30 \text{ years}\]
4. Calculate the future value (\(FV\)) using the formula: \[FV = PV + \sum_{i=1}^{30} (5,000 \times (1 + 0.07)^i)\] \[FV = \$10,000 + \$5,000 \times \left(\frac{(1 + 0.07)^{30} - 1}{0.07}\right)\] \[FV = \$10,000 + \$5,000 \times 94.461\] \[FV = \$10,000 + \$472,305\] \[FV = \$482,305\]

Example Calculation

Let's calculate the future value of an investment for an individual with the following details:

• Initial Investment (\(PV\)): $10,000
• Return Amount: $5,000
• Rate of Return (\(r\)): 7%
• Number of Years (\(n\)): 30 years

Using the formula, we get:

1. Initial investment: \(PV = \$10,000\)
2. Return amount: \(C = \$5,000\)
3. Rate of return: \(r = 7\%\)
4. Number of years: \(n = 30\)
5. Future value: \[FV = 10,000 + \sum_{i=1}^{30} (5,000 \times (1 + 0.07)^i)\] \[FV = \$10,000 + \$5,000 \times \left(\frac{(1 + 0.07)^{30} - 1}{0.07}\right)\] \[FV = \$10,000 + \$5,000 \times 94.461\] \[FV = \$10,000 + \$472,305\] \[FV = \$482,305\]

Visual Representation

The green portion of the bar represents the calculated future value ($482,305) relative to the maximum possible value.