# Systematic Investment Plan

## Systematic Investment Plan

**Systematic Investment Plan (SIP)** is a method of investing a fixed sum regularly in a mutual fund. SIPs are designed to encourage disciplined investment, allowing investors to accumulate wealth over time through regular, smaller investments.

#### Formula to Calculate SIP Returns

The formula to calculate the future value of SIP investments is:

\[ A = P \times \left( \frac{(1 + r)^n – 1}{r} \right) \times (1 + r) \]

Where:

**A**: The amount of money accumulated after n months, including interest.**P**: The amount invested at regular intervals.**r**: The periodic interest rate (annual interest rate divided by 12).**n**: The total number of payments (investment periods).

#### Example of Calculating SIP Returns

Assume you invest $500 every month in a mutual fund with an annual interest rate of 12%. The interest rate per month would be:

\[ r = \frac{12\%}{12} = 1\% = 0.01 \]

If you invest for 5 years (60 months), the future value of the SIP would be calculated as follows:

\[ n = 5 \times 12 = 60 \]

\[ A = 500 \times \left( \frac{(1 + 0.01)^{60} – 1}{0.01} \right) \times (1 + 0.01) \]

**Calculating step-by-step:**

1. Calculate \((1 + 0.01)^{60}\):

\[ (1 + 0.01)^{60} \approx 1.816 \]

2. Subtract 1:

\[ 1.8167 – 1 = 0.8167 \]

3. Divide by 0.01:

\[ \frac{0.816}{0.01} = 81.67 \]

4. Multiply by the monthly investment and add the final month’s interest:

\[ 500 \times 81.67 \times 1.01 = 41,243\]

So, the future value of the SIP after 5 years would be approximately $41,243