Simple Interest Formula and Problems

Simple interest is earned only on the original sum, the principal. Each year the same amount of interest is added, so the money grows in a straight line. That is what makes these problems quick: once you know one year's interest, you know every year's.

SI = P × R × T ÷ 100, and Amount = P + SI

Here P is the principal in rupees, R is the rate per cent per year, and T is the time in years. Any one of SI, P, R and T can be found if the other three are known, by rearranging the same formula.

Worked example 1: interest

₹8,000 is lent at 6% for 3 years. SI = 8,000 × 6 × 3 ÷ 100 = ₹1,440, and the amount is ₹9,440.

To find	Formula
Rate	R = SI × 100 ÷ (P × T)
Time	T = SI × 100 ÷ (P × R)
Principal from SI	P = SI × 100 ÷ (R × T)
Principal from amount	P = Amount × 100 ÷ (100 + R × T)

Worked example 2: the rate

₹9,000 earns ₹2,700 in 3 years. R = 2,700 × 100 ÷ (9,000 × 3) = 10% per year.

Worked example 3: principal from the amount

A sum amounts to ₹7,800 in 3 years at 10%. The total interest is 30% of P, so the amount is 130% of P. P = 7,800 × 100 ÷ 130 = ₹6,000.

Do not subtract 30% of ₹7,800 to find the principal. The percentage is of P, which is the unknown, not of the amount.

A favourite exam pattern gives the amount after one period and after a longer one. The difference between the two amounts is the interest for the extra years, which gives one year's interest. Subtract the interest for the first period from the first amount to recover P.

Worked example 4: ₹6,720 and ₹7,440

A sum becomes ₹6,720 in 2 years and ₹7,440 in 5 years. The 3 extra years earn ₹720, so one year earns ₹240. Two years earn ₹480, so P = 6,720 − 480 = ₹6,240.

A sum doubles when the interest equals the principal, that is, when R × T = 100. It becomes n times itself when the interest equals (n − 1) × P, that is, when R × T = 100 × (n − 1).

Worked example 5: doubling in 8 years

R × 8 = 100, so R = 12.5%.

At the same rate the sum triples when the interest is 2 × P, which takes 2 × 8 = 16 years. The times for doubling, tripling and quadrupling are in the ratio 1 : 2 : 3.

Worked example 6: five times in 20 years

The interest is 4 × P, so R × 20 = 400 and R = 20%.

Time must be in years, so convert months by dividing by 12. When the rate changes partway, work out the interest for each period separately and add.

Worked example 7: 8 months

₹12,000 at 9% for 8 months: SI = 12,000 × 9 × 8/12 ÷ 100 = ₹720.

Worked example 8: two rates

₹5,000 is lent at 8% for 2 years and then at 10% for 3 more years. The interest is 800 + 1,500 = ₹2,300. Because simple interest never earns interest on interest, the periods simply add.

A related pattern splits one sum between two rates and gives the total interest for a year. Suppose all of it were lent at the higher rate; the shortfall from that interest is caused entirely by the part at the lower rate. Divide the shortfall by the difference in rates to find that part.

Worked example 9: one sum at two rates

₹10,000 is split, with part at 8% and the rest at 12%, and the year's interest is ₹1,040. At 12% throughout it would be ₹1,200. The shortfall of ₹160 comes from a 4% gap, so the part at 8% is 160 × 100 ÷ 4 = ₹4,000.

✘ Using months as T without dividing by 12.
✘ Finding P by taking a percentage of the amount instead of dividing by (100 + RT).
✘ Thinking a sum that doubles in 8 years quadruples in 16. It needs 3 × 8 = 24 years.
✘ Applying simple interest logic to compound interest questions.

Once simple interest is clear, compare it with compound interest for different compounding periods and the CI and SI difference formula. The key results are listed in the Quant cheat code.

Q1. What is the simple interest on ₹15,000 at 7% per annum for 4 years? easy

(a) ₹3,800 (b) ₹4,200 (c) ₹4,500 (d) ₹1,050

✅ Answer: (b) ₹4,200

💡 Explanation: SI = P × R × T ÷ 100 = 15,000 × 7 × 4 ÷ 100 = ₹4,200. ₹1,050 is the interest for one year only.

Q2. A sum of money doubles itself in 10 years at simple interest. What is the rate of interest? easy

(a) 5% (b) 20% (c) 12.5% (d) 10%

✅ Answer: (d) 10%

💡 Explanation: Doubling means the interest equals the principal, which is 100% of P. Spread over 10 years that is 100 ÷ 10 = 10% per year.

Q3. A sum amounts to ₹9,800 in 4 years at 10% per annum simple interest. What is the sum? medium

(a) ₹7,000 (b) ₹8,820 (c) ₹6,860 (d) ₹7,500

✅ Answer: (a) ₹7,000

💡 Explanation: In 4 years at 10% the amount is 140% of the principal. P = 9,800 × 100 ÷ 140 = ₹7,000.

Q4. A sum amounts to ₹8,280 in 3 years and ₹9,000 in 5 years at simple interest. What is the sum? medium

(a) ₹7,560 (b) ₹7,000 (c) ₹7,200 (d) ₹7,920

✅ Answer: (c) ₹7,200

💡 Explanation: The extra 2 years earn 9,000 − 8,280 = ₹720, so one year's interest is ₹360. Three years' interest is ₹1,080, so P = 8,280 − 1,080 = ₹7,200.

Q5. A sum doubles in 6 years at simple interest. In how many years will it become 4 times itself? hard

(a) 18 years (b) 12 years (c) 24 years (d) 15 years

✅ Answer: (a) 18 years

💡 Explanation: Doubling means the interest equals 1 × P in 6 years. Becoming 4 times needs interest of 3 × P, which takes 3 × 6 = 18 years.

Q6. What is the simple interest on ₹6,000 at 12% per annum for 1 year 3 months? medium

(a) ₹720 (b) ₹780 (c) ₹960 (d) ₹900

✅ Answer: (d) ₹900

💡 Explanation: 1 year 3 months is 15 ÷ 12 = 1.25 years. SI = 6,000 × 12 × 1.25 ÷ 100 = ₹900.

Why does a sum take twice as long to triple as it takes to double?

Under simple interest the same amount is added every year. Doubling adds one principal of interest and tripling adds two principals, so tripling takes exactly twice as long. This is not true for compound interest.

Should I convert months and days into years?

Yes. The rate in the formula is per year, so time must be in years. Divide months by 12. For days, divide by 365 unless the question tells you to use a different convention.

All problems and solutions on this page are original. No outside facts are relied on; every numeric answer is recomputed by software before publishing.

How this page was prepared. Drafted with AI assistance (Claude (Anthropic AI model)) from the sources listed above. 16 calculations on this page were recomputed by software and matched. Automated checks also covered structure, internal links and duplicate text. Software checks cannot confirm facts. Reviewed by praveenkumar on 2026-10-20 against the sources listed above.

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