Simple Interest Formula
SI = (P × R × T) / 100 — how interest is calculated on a fixed principal
The formula
P is the principal — the amount lent or borrowed at the start. R is the annual rate of interest, expressed as a percentage (not a decimal). T is the time in years. SI is the simple interest accumulated over the period. The total amount at the end (A) is P + SI.
What is Simple Interest?
Simple interest is the most basic way to calculate the cost of borrowing money or the reward for saving it. Unlike compound interest, the amount of interest earned or charged each year stays exactly the same — it's calculated on the original principal only, never on accumulated interest. That's what makes it "simple": each year's interest is a fixed percentage of the starting amount.
The formula has a factor of 100 in the denominator because the rate is written as a percentage. If your rate is 8% and you prefer working in decimals, you can drop the /100 and use R = 0.08 directly. Either form works — just be consistent within a single calculation. Some textbooks write the formula as I = Prt with R in decimal form; others keep the /100 in the formula and expect R in percent. Check which convention your course uses before plugging in numbers.
Simple interest shows up in short-term loans (personal loans under a year, most government bonds held to coupon date, certain auto loan promotions), fixed deposits in some banking products, and school and entrance-exam problems in the percentages / aptitude sections. For long-term savings and most modern loans you'll meet compound interest instead, because compounding produces a materially larger number once the time period stretches beyond a year or two.
Two things worth memorising: the total amount formula A = P(1 + RT/100) is just principal plus simple interest combined, and the formula rearranges cleanly in every direction — given any three of P, R, T and SI you can solve for the fourth by moving the others to the other side of the equals sign. Aptitude exams frequently hide the unknown inside a word problem where the principal or the rate is the missing quantity, not the interest itself.
Solved Examples
Example 1: Find the simple interest on ₹12,000 at 8% per annum for 3 years.
- 1
Identify the variables
P = 12,000, R = 8, T = 3. We want SI.
- 2
Substitute into the formula
- 3
Simplify the numerator
The 100 in the denominator divides out cleanly here.
Answer
SI = ₹2,880
Example 2: A sum of money doubles itself in 8 years at simple interest. Find the rate of interest per annum.
- 1
Translate 'doubles itself' into an equation
If the principal doubles, the simple interest earned equals the principal. So SI = P when T = 8.
- 2
Plug SI = P into the formula and solve for R
Dividing both sides by P cancels it out — the answer doesn't depend on the actual amount invested.
- 3
Solve
Answer
The rate of interest is 12.5% per annum.
Example 3: How long will it take for ₹5,000 to earn ₹1,125 in simple interest at 9% per annum?
- 1
List the knowns and unknowns
P = 5,000, R = 9, SI = 1,125. We want T in years.
- 2
Rearrange the formula for T
Move P and R to the other side and multiply SI by 100.
- 3
Compute
Two-and-a-half years means 2 years and 6 months.
Answer
T = 2.5 years (2 years 6 months)
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