Simple Interest

SI formula, principal, rate, time

103 practice questionsPage updated 1 Sept 2026Reviewed by AISEA Editorial DeskPractice questions

Simple interest is calculated only on the original principal for the full stated period. It grows linearly with principal, rate and time, so each year at a fixed rate contributes the same interest. In aptitude questions, first separate principal, interest and final amount, then put the rate and time in compatible units before solving for the unknown.

Key formulas and rules

Simple interest: SI = (P × R × T) / 100, when R is a percentage rate per annum and T is in years.

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

Rate: R = 100SI / (P × T).

Time: T = 100SI / (P × R).

Principal: P = 100SI / (R × T).

For m months: SI = (P × R × m) / (100 × 12).

If A = kP, then SI = (k − 1)P and R = 100(k − 1) / T.

For the same P and T, difference in interest = P × difference in rate × T / 100.

If amounts at two times use the same simple-interest rate, annual interest = (later amount − earlier amount) / time gap in years.

Key concepts

Identify P, R, T, SI and A

P is the original principal, R is the annual rate expressed as a percentage, T is time in years, SI is interest alone and A is the final amount. The central relationship is A = P + SI. Write these five quantities in a small list before substituting numbers so that amount is not mistaken for interest.

Simple interest versus compound interest

Under simple interest, every period's interest is based on the original principal. Under compound interest, later interest can be based on a principal that includes earlier interest. Use the simple-interest formula only when the question explicitly says simple interest or gives a context that defines it; do not compound the amount between periods.

Worked examples

Example 1

Find the simple interest on ₹5,000 at 8% per annum for 3 years.

Solution

Step 1: P = ₹5,000, R = 8 and T = 3 years.
Step 2: SI = (P × R × T) / 100 = (5,000 × 8 × 3) / 100.
Step 3: SI = ₹1,200.
Answer: ₹1,200.

Example 2

A sum of ₹6,000 amounts to ₹7,200 in 4 years at simple interest. Find the annual rate.

Solution

Step 1: SI = A − P = ₹7,200 − ₹6,000 = ₹1,200.
Step 2: R = 100SI / (P × T) = (100 × 1,200) / (6,000 × 4).
Step 3: R = 5%.
Answer: 5% per annum.

Example 3

What principal will amount to ₹7,000 in 4 years at 10% per annum simple interest?

Solution

Step 1: A = P(1 + RT / 100) = P(1 + 10 × 4 / 100) = 1.4P.
Step 2: 7,000 = 1.4P.
Step 3: P = 7,000 / 1.4 = ₹5,000.
Step 4: Check: interest is ₹2,000 and principal plus interest is ₹7,000.
Answer: ₹5,000.

Example 4

A sum amounts to ₹5,400 in 3 years and ₹6,200 in 5 years at simple interest. Find the principal.

Solution

Step 1: Interest for the 2-year gap = ₹6,200 − ₹5,400 = ₹800.
Step 2: Interest per year = ₹800 / 2 = ₹400.
Step 3: Interest for the first 3 years = 3 × ₹400 = ₹1,200.
Step 4: Principal = ₹5,400 − ₹1,200 = ₹4,200.
Answer: ₹4,200.

Example 5

Find the simple interest on ₹12,000 for 8 months at 15% per annum.

Solution

Step 1: Convert time: T = 8 / 12 = 2 / 3 years.
Step 2: SI = (12,000 × 15 × 2 / 3) / 100.
Step 3: SI = ₹1,200.
Answer: ₹1,200.

Example 6

At what annual rate will a principal double itself in 8 years at simple interest?

Solution

Step 1: If A = 2P, then SI = A − P = P.
Step 2: P = (P × R × 8) / 100. Cancel P: 1 = 8R / 100.
Step 3: R = 100 / 8 = 12.5%.
Answer: 12.5% per annum.

Example 7

₹15,000 is split between investments at 8% and 12% per annum simple interest. If the total annual interest is ₹1,440, how much is invested at 8%?

Solution

Step 1: Let x be invested at 8%; ₹15,000 − x is invested at 12%.
Step 2: Annual interest equation: 0.08x + 0.12(15,000 − x) = 1,440.
Step 3: 0.08x + 1,800 − 0.12x = 1,440, so 0.04x = 360.
Step 4: x = ₹9,000.
Answer: ₹9,000 is invested at 8%.

Example 8

₹12,000 is invested for 2 years at 8% per annum and for the next 2 years at 12% per annum simple interest. Find the final amount, assuming interest is calculated on the original principal throughout.

Solution

Step 1: First-period interest = (12,000 × 8 × 2) / 100 = ₹1,920.
Step 2: Second-period interest = (12,000 × 12 × 2) / 100 = ₹2,880.
Step 3: Total interest = ₹1,920 + ₹2,880 = ₹4,800.
Step 4: Final amount = ₹12,000 + ₹4,800 = ₹16,800.
Answer: ₹16,800.

Example 9

The difference between the simple interest from two banks on ₹5,000 for 4 years is ₹200. Find the difference between their annual rates.

Solution

Step 1: Difference in SI = P × difference in rate × T / 100.
Step 2: 200 = (5,000 × ΔR × 4) / 100 = 200ΔR.
Step 3: ΔR = 1.
Answer: The rates differ by 1 percentage point per annum.

Example 10

A person borrows ₹5,000 at 4% per annum simple interest for 2 years and lends it at 6% for the same period. Find the gain.

Solution

Step 1: Interest paid = (5,000 × 4 × 2) / 100 = ₹400.
Step 2: Interest earned = (5,000 × 6 × 2) / 100 = ₹600.
Step 3: Gain = ₹600 − ₹400 = ₹200.
Answer: ₹200.

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Simple Interest

Key formulas and rules

Key concepts

Identify P, R, T, SI and A

Simple interest versus compound interest

Keep rate and time compatible

Solve for the missing variable

Use amount differences to remove the principal

Handle multiple rates on one principal

Use multiples of the principal

Compare rates, returns and lending gains

Check units, rounding and reasonableness

Worked examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Sources and review notes

Ready to test your understanding?

Key formulas and rules

Key concepts

Identify P, R, T, SI and A

Simple interest versus compound interest

Keep rate and time compatible

Solve for the missing variable

Use amount differences to remove the principal

Handle multiple rates on one principal

Use multiples of the principal

Compare rates, returns and lending gains

Check units, rounding and reasonableness

Worked examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Sources and review notes

Ready to test your understanding?

Keep building the same skill family.