Mathematics • 5 min read

SIP Calculator: Understanding the Math Behind It

Information Disclaimer: This article is strictly for educational, factual, and mathematical illustration purposes. It does not contain financial advice, tax guidance, or investment recommendations. All mutual fund investments are subject to market risks.

1. The Future Value of Annuity Formula

Online calculators use the **Future Value of an Annuity Due** formula to project the growth of periodic, automated monthly payments. The formula assumes that installments are deposited at the beginning of each monthly compounding period.

FV = P × [ ( (1 + i)^n - 1 ) / i ] × (1 + i)

Where:

  • FV = Future Value (total maturity amount)
  • P = Monthly investment amount
  • i = Monthly interest rate (Annual Return Rate / 12 / 100)
  • n = Total number of monthly installments (Years × 12)

2. Step-by-Step Manual Walkthrough

Let us calculate the future value of a **₹1,000 monthly SIP** for a duration of **3 months** assuming an annual return rate of **12% p.a.**:

1. Find Monthly Interest Rate (i):

i = 12% / 12 months = 1% per month = 0.01

2. Define Installments (n):

n = 3 months

3. Define Installment Amount (P):

P = ₹1,000

Now, let us calculate the future value of each of the three monthly payments individually, based on how long each payment compounds:

  • Installment 1 (deposited at start of Month 1): Compounds for exactly 3 months.
    FV1 = 1,000 × (1 + 0.01)^3 = 1,000 × 1.0303 = ₹1,030.30
  • Installment 2 (deposited at start of Month 2): Compounds for exactly 2 months.
    FV2 = 1,000 × (1 + 0.01)^2 = 1,000 × 1.0201 = ₹1,020.10
  • Installment 3 (deposited at start of Month 3): Compounds for exactly 1 month.
    FV3 = 1,000 × (1 + 0.01)^1 = 1,000 × 1.0100 = ₹1,010.00
Total Future Value = FV1 + FV2 + FV3 = 1,030.30 + 1,020.10 + 1,010.00 = ₹3,060.40

3. Verifying Using the Annuity Formula

Let us verify the manual calculation using the rearranged annuity formula:

FV = 1,000 × [ ( (1 + 0.01)^3 - 1 ) / 0.01 ] × (1 + 0.01)

FV = 1,000 × [ ( 1.030301 - 1 ) / 0.01 ] × 1.01

FV = 1,000 × [ 0.030301 / 0.01 ] × 1.01

FV = 1,000 × 3.0301 × 1.01

FV = 3,030.10 × 1.01 = ₹3,060.40

Both methods yield the exact same output of **₹3,060.40**. Out of this, the total invested capital is **₹3,000.00** (₹1,000 × 3), and the compounded return is **₹60.40**. Online calculators use this consolidated formula to perform similar calculations instantly over longer periods (such as 10, 20, or 30 years).