Simple Interest: Meaning, Core Formulae & Commercial Calculations

1. Concept of Interest and Commercial Terminology

When money is borrowed from a lender or deposited in a financial institution, the borrower pays consideration for the privilege of utilizing capital over a specified time. This additional compensation is called Interest.

2. Core Formulae of Simple Interest

In Simple Interest, the interest earned remains uniform year after year because the principal base does not change:

Simple Interest (SI) = (P × R × T) ÷ 100
Total Amount (A) = P + SI = P × [ 1 + (R × T) ÷ 100 ]

Derived Formulae for Unknown Variables:

3. Day-Count Conventions in Commercial Practice

When loans are contracted for short periods, time T is specified in days. Indian commercial banking distinguishes two conventions:

1. Exact Simple Interest (365-Day Year):
   • T = Number of Days ÷ 365 (or 366 in a leap year)
   • Standard convention across Indian commercial banking and government treasury operations.
2. Ordinary / Banker’s Interest (360-Day Year):
   • T = Number of Days ÷ 360
   • Assumes 12 uniform months of 30 days each. Yields slightly higher interest for the lender.

[!NOTE] When counting days between two dates, exclude the starting date and include the maturity date (or vice versa).

4. Worked Business Problems

Problem 1: Basic Simple Interest & Amount

Question: A trading firm borrows ₹80,000 from a commercial bank at 9.5% per annum simple interest for 3 years and 6 months. Calculate the total interest payable and the final settlement amount.

Step-by-Step Solution:

1. Identify variables:
   • Principal (P) = ₹80,000
   • Rate (R) = 9.5% per annum
   • Time (T) = 3 years + 6 months = 3.5 years
2. Compute Simple Interest:
   • SI = (P × R × T) ÷ 100
   • SI = (80,000 × 9.5 × 3.5) ÷ 100
   • SI = 2,660,000 ÷ 100 = ₹26,600
3. Compute Total Maturity Amount:
   • A = P + SI = 80,000 + 26,600 = ₹1,06,600
   • Conclusion: Total interest is ₹26,600 and final amount is ₹1,06,600.

Problem 2: Finding Principal when Amount is Given

Question: A sum of money invested at 7% per annum simple interest amounts to ₹37,200 in 4 years. What was the principal sum originally invested?

Step-by-Step Solution:

1. Use the Amount Formula:
   • A = P × [ 1 + (R × T) ÷ 100 ]
   • 37,200 = P × [ 1 + (7 × 4) ÷ 100 ]
   • 37,200 = P × [ 1 + 0.28 ] = 1.28 × P
2. Solve for P:
   • P = 37,200 ÷ 1.28 = ₹29,062.50
   • Conclusion: The principal originally invested was ₹29,062.50.

Problem 3: Multi-Period Varying Rates

Question: A cooperative credit society lends ₹50,000 to an entrepreneur on the terms: 6% p.a. for the first 2 years, 8% p.a. for the next 3 years, and 11% p.a. for any period beyond 5 years. If the loan is cleared after 7 years, compute total interest.

Step-by-Step Solution:

1. Period 1 (First 2 years at 6%):
   • SI₁ = (50,000 × 6 × 2) ÷ 100 = ₹6,000
2. Period 2 (Next 3 years at 8%):
   • SI₂ = (50,000 × 8 × 3) ÷ 100 = ₹12,000
3. Period 3 (Remaining 2 years at 11%):
   • SI₃ = (50,000 × 11 × 2) ÷ 100 = ₹11,000
4. Total Accumulated Simple Interest:
   • Total SI = 6,000 + 12,000 + 11,000 = ₹29,000
   • Conclusion: Total simple interest payable is ₹29,000.

5. Summary Cheat Sheet for Examinations