Simple Interest: Formula, Methods and Solved Examples

Simple Interest is calculated only on the original principal throughout the time period. This page covers the simple interest formula, amount calculation, conversion of months into years, and methods for finding the principal, rate, or time. It also includes SI shortcuts and numerical examples for interest calculation.

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What Is Simple Interest?

Simple Interest is the interest calculated on the original principal for the entire time period. It does not include previously earned interest in the principal for later calculations.

For principal P, annual rate R percent, and time T years, simple interest is SI = (P × R × T) / 100. The total amount is A = P + SI. If time is given in months, convert it into years using T = months / 12, provided the rate is annual.

Simple Interest Formula & Tricks

Important Formulas

Simple Interest
SI = (P × R × T) / 100

Use this when P is the principal, R is the annual rate in percent, and T is time in years.

Amount
A = P + SI = P(1 + RT/100)

The amount is the total sum received after adding simple interest to the principal.

Principal
P = (100 × SI) / (R × T)

Use this formula when simple interest, rate, and time are known.

Rate
R = (100 × SI) / (P × T)

This gives the annual rate in percent when principal, simple interest, and time are known.

Time
T = (100 × SI) / (P × R)

This gives time in years when principal, rate, and simple interest are known.

Quick Tricks

Convert months into years before applying the formula

When the annual rate is given, divide the number of months by 12. For example, 9 months means T = 9/12 = 3/4 year.

Example: For P = ₹8,000, R = 10% per year, and T = 9 months, SI = 8000 × 10 × 3/(4 × 100) = ₹600.
Use proportionality for equal principal and rate

At fixed principal and rate, simple interest is directly proportional to time. Therefore, interest for 3 years is three times the interest for 1 year.

Example: If the SI for 1 year is ₹450, the SI for 3 years is ₹1,350.
Find the interest fraction of the principal

SI/P = RT/100. Thus, when rate and time are known, simple interest can be found as a fixed fraction of the principal.

Example: At 8% per year for 5 years, SI/P = 8 × 5/100 = 2/5. For P = ₹2,500, SI = ₹1,000.

Simple Interest Concepts

Calculating Simple Interest from Principal, Rate and Time

Multiply the principal, annual rate, and time in years, then divide the product by 100.

Use SI = (P × R × T)/100 when the rate is expressed as a percentage. The principal and interest must have the same currency unit, while time must match the rate period.

Example: For P = ₹12,000, R = 7.5% per year, and T = 2 years, SI = (12000 × 7.5 × 2)/100 = ₹1,800.

Finding the Total Amount

The total amount is the original principal plus the simple interest: A = P + SI.

Substituting the SI formula gives A = P(1 + RT/100). The amount is greater than the principal when the rate and time are positive.

Example: If P = ₹5,000 and SI = ₹750, then A = 5000 + 750 = ₹5,750.

Finding Principal, Rate or Time

Rearrange SI = PRT/100 to find any missing quantity.

Use P = 100SI/(RT), R = 100SI/(PT), or T = 100SI/(PR). The value of T obtained from this formula is in years when R is an annual percentage rate.

Example: If SI = ₹960, R = 8% per year, and T = 3 years, P = (100 × 960)/(8 × 3) = ₹4,000.

Time Conversion and Rate Period

The time unit must match the period used for the interest rate.

For an annual rate, convert months into years by dividing by 12 and days into years according to the convention specified in the question. If the rate is monthly, time may be used in months without conversion.

Example: At 12% per year for 6 months, T = 6/12 = 1/2 year. For P = ₹10,000, SI = 10000 × 12 × 1/2 / 100 = ₹600.

Difference Between Simple Interest and Amount

Simple interest is only the extra money earned or paid, whereas amount includes both principal and interest.

The relation is A = P + SI, so SI = A − P. Confusing A with SI leads to an excess of the principal in the answer.

Example: If the amount is ₹9,200 and the principal is ₹8,000, then SI = 9200 − 8000 = ₹1,200.

Simple Interest Video Lessons

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6 Lessons
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Simple Interest Formula: Find P, R, T

Learn how to use the simple interest formula to calculate Principal (P), Rate (R), or Time (T) when the other values are given.

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Practice Simple Interest Questions

Practise published questions related to this topic.

1Cost price of 25 articles is Rs. 197. Selling price of 30 articles is Rs. 197. What is the ratio of the value of profit/loss of 1 article to the selling price of 1 article? (Cost price of all the articles is same. Selling price of all the articles is same.)→ 2Manju sold a scooty with a tagged price of ₹1,25,000 . After applying a trade concession, the final transaction value became ₹70,000 . Calculate the percentage discount given on the marked price.→ 3Evaluate: 3⁵ × 7⁵ ÷ 21³→ 4√625 + √0.25 + √0.0004 = ?→ 5A scheme like 'Buy 6, Get 2 Free' on the same kind of articles with the same MRP attracts a _____ % discount.890→ 6A dealer makes a profit of 40% even after giving a 26% discount on the advertised price of a bike. If he makes a profit of ₹5,698 on the sale of the bike, what is the advertised price (in ₹)?435→ 7Simplify the expression: (3^((4+x)) × 9^((x-4)))/(27^((x-3)) × 3³)→ 8A person earns 20 percent profit on selling price. What is the ratio of the value of the profit to the cost price of the article?→ 9What is the square root of 4900?→ 10The Highest Common Factor (HCF) of two numbers is 48 and their Least Common Multiple (LCM) is 3456. If one of the numbers is 768, find the other number.→

Simple Interest Quick Quiz

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Quick Revision Notes

Simple Interest Revision Points

Use these formulas and rules for quick revision.

  • SI = (P × R × T)/100 when R is in percent and T is in years.
  • Amount A = P + SI.
  • For an annual rate, convert m months to T = m/12 years.
  • P = 100SI/(RT), R = 100SI/(PT), and T = 100SI/(PR).
  • SI is calculated on the original principal only; previously earned interest is not added to the principal.
  • Keep the time unit consistent with the rate period.
  • SI/P = RT/100, so interest is directly proportional to principal, rate, and time when the other two quantities remain fixed.

Simple Interest FAQs

What is the simple interest formula?

The formula is SI = (P × R × T)/100, where P is principal, R is annual rate in percent, and T is time in years.

How is simple interest calculated for months?

Convert months into years when the rate is annual: T = months/12. For ₹6,000 at 10% per year for 4 months, SI = 6000 × 10 × 4/(12 × 100) = ₹200.

What is the difference between simple interest and amount?

Simple interest is the interest alone. Amount is principal plus interest, so A = P + SI.

How do you find the principal from simple interest?

Use P = 100SI/(RT). For SI = ₹900, R = 6%, and T = 2.5 years, P = 100 × 900/(6 × 2.5) = ₹6,000.

How do you find the rate in a simple interest problem?

Use R = 100SI/(PT). If P = ₹4,000, SI = ₹800, and T = 5 years, R = 100 × 800/(4000 × 5) = 4% per year.

How does simple interest change when the time is doubled?

For fixed principal and rate, simple interest is directly proportional to time. Doubling the time doubles the simple interest.

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