Simple Interest and Compound Interest: Formulas, Rules and Examples

Simple Interest and Compound Interest calculate the return earned on a principal over time. Simple interest is calculated only on the original principal, while compound interest is calculated on the accumulated amount. This page covers SI and CI formulas, amount calculation, conversion of compounding periods, the difference between SI and CI, and useful numerical shortcuts.

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What are Simple Interest and Compound Interest?

Simple Interest is calculated only on the original principal throughout the interest period. Compound Interest is calculated on the principal plus the interest accumulated in previous periods.

Let P be the principal, R the annual rate of interest in percent, T the time in years, and A the final amount. For simple interest, SI = (P × R × T)/100 and A = P + SI. For annual compounding, A = P(1 + R/100)^T and CI = A − P. For example, on ₹5,000 at 10% per annum for 2 years, SI is ₹1,000, whereas annual CI is ₹1,050.

Simple Interest and Compound Interest Formula & Tricks

Important Formulas

Simple Interest
SI = (P × R × T)/100

Use P in rupees, R as the annual percentage rate, and T in years.

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

The amount is the principal plus the simple interest.

Compound Amount
A = P(1 + R/100)^T

This formula applies when interest is compounded annually and T is in years.

Compound Interest
CI = A − P = P[(1 + R/100)^T − 1]

Subtract the original principal from the compound amount.

Compounding m times per year
A = P(1 + R/(100m))^(mT)

For m compounding periods per year, divide the annual rate by m and multiply the number of years by m.

Difference for two years
CI − SI = P(R/100)^2

For a two-year period with annual compounding, the difference is P × R²/10,000.

Quick Tricks

Two-year SI–CI shortcut

For two years, avoid calculating both amounts separately. The difference between compound interest and simple interest is P × R²/10,000.

Example: For P = ₹8,000 and R = 5%, difference = 8,000 × 25/10,000 = ₹20.
Convert the period before applying the formula

For months, use T = months/12 in annual formulas. For half-yearly compounding, use rate R/2 and time 2T periods.

Example: At 12% per annum compounded half-yearly for 1 year, use 6% per half-year for 2 periods: A = P(1.06)^2.
Successive growth factors for compound interest

Apply the growth factor separately for each period. A rate of R% per period multiplies the amount by (1 + R/100).

Example: ₹10,000 growing at 10% for two periods becomes 10,000 × 1.10 × 1.10 = ₹12,100.

Simple Interest and Compound Interest Concepts

Simple Interest Calculation

Simple interest remains based on the original principal, so the interest earned in every equal period is the same.

The simple interest for T years is SI = (P × R × T)/100. The amount is A = P + SI. If the time is given in months, convert it to years using T = months/12. If the rate is given for a different period, express the time in the same period before calculating.

Example: For ₹6,000 at 8% per annum for 9 months, SI = 6,000 × 8 × (9/12)/100 = ₹360, so A = ₹6,360.

Compound Interest with Annual Compounding

Under annual compounding, each year's interest is added to the amount, and the next year's interest is calculated on this increased amount.

For annual compounding, A = P(1 + R/100)^T and CI = A − P. The interest is not equal in every year because the base increases after each compounding period.

Example: For ₹10,000 at 10% per annum for 2 years, A = 10,000(1.10)^2 = ₹12,100 and CI = ₹2,100.

Difference Between SI and CI

For the same principal, rate and period, compound interest is greater than simple interest when the time exceeds one compounding period.

For two years with annual compounding, CI − SI = P(R/100)^2. For three years, the difference is P[3(R/100)^2 + (R/100)^3]. The difference occurs because compound interest earns interest on previously added interest.

Example: For ₹5,000 at 10% for 2 years, SI = ₹1,000 and CI = ₹1,050. Therefore, CI − SI = ₹50, also equal to 5,000 × 10²/10,000.

Half-Yearly and Quarterly Compounding

When interest is compounded more than once a year, divide the annual rate by the number of compounding periods and multiply the time by that number.

For m compounding periods per year, A = P(1 + R/(100m))^(mT). Thus, for half-yearly compounding use R/2 per half-year; for quarterly compounding use R/4 per quarter. The annual percentage rate is converted to the rate applicable to one compounding period.

Example: For ₹20,000 at 8% per annum compounded half-yearly for 1 year, A = 20,000(1 + 8/200)^2 = 20,000(1.04)^2 = ₹21,632; CI = ₹1,632.

Rate or Time from Interest and Amount

Under simple interest, the unknown rate or time can be found by rearranging SI = (P × R × T)/100.

The rearranged forms are R = (100 × SI)/(P × T) and T = (100 × SI)/(P × R). Under compound interest, first use A/P = (1 + R/100)^T and then solve for the unknown quantity when required.

Example: If P = ₹4,000, SI = ₹640 and T = 2 years, R = (100 × 640)/(4,000 × 2) = 8% per annum.

Simple Interest and Compound Interest Video 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 and Compound Interest Questions

Practise published questions related to this topic.

1A shopkeeper offers the following schemes on toys of the same marked price. (A) Successive discounts of 50% and 16% on any number of toys bought. (B) Successive discounts of 49%, 8% and 13% on any number of toys bought. (C) 35% discount on the first 6 toys and 45% discount on each toy thereon. (D) On buying eight items, the customer is billed for only four items. A customer wants to buy 8 toys. Which of the above schemes is the least beneficial to her?→ 2The simplified value of the expression 0.5² × 5⁵ × 2⁻⁴ × 4⁴ × 10⁻³ ÷ a is 1, then the value of a is ______.→ 3A shopkeeper offers a fixed discount of 15% on rice and 100 gm rice free with every purchase of 1.9 kg rice. Find the overall discount percent offered by him on rice.→ 4The number 8,33,525 is NOT divisible by:→ 5What is the smallest number that, when divided by 2, 3, 4, 5, 6, and 7 leaves remainder 1?→ 6A dealer purchased a laptop for ₹99,000. He allows a discount of 37% on its marked price and still gains 40%. Find the marked price of the laptop.→ 7Find the effective price percentage of the marked price after three consecutive discounts of 10%, 27% and 8% (rounded off to two decimal places).→ 8A shopkeeper offers the following schemes on toys of the same marked price. (A) Successive discounts of 24% and 33% on any number of toys bought. (B) Successive discounts of 39%, 37% and 23% on any number of toys bought. (C) 24% discount on the first 2 toys and 12% discount on each toy thereon. (D) 2 toys free of cost on buying 5 toys. A customer wants to buy 5 toys. Which of the above schemes is the least beneficial to her?→ 9A shopkeeper marks a washing machine at ₹24,000. During a festival, he offers a 20% discount and sells it for an additional ₹800 less. What is the final selling price of the washing machine?→ 10The HCF and LCM of two positive integers are 36 and 7,560, respectively. If one of the numbers is 540, what is the other number?→

Simple Interest and Compound Interest Quick Quiz

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Quick Revision Notes

Simple Interest and Compound Interest Revision Points

Remember these formulas, conversions and comparison rules while solving interest questions.

  • SI = (P × R × T)/100 and amount under SI is P + SI.
  • For annual CI, A = P(1 + R/100)^T and CI = A − P.
  • For m compounding periods per year, use rate R/m per period and mT total periods.
  • Convert months into years for annual simple-interest formulas: T = months/12.
  • For two years with annual compounding, CI − SI = P × R²/10,000.
  • For the same P, R and T, CI exceeds SI when there is more than one compounding period.
  • Always distinguish between interest and amount: amount = principal + interest.

Simple Interest and Compound Interest FAQs

What is the formula for simple interest?

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

What is the formula for compound interest with annual compounding?

First find A = P(1 + R/100)^T. Then CI = A − P.

How is compound interest calculated for half-yearly compounding?

Use half the annual rate for each half-year and twice the number of years as the number of periods: A = P(1 + R/200)^(2T).

What is the difference between SI and CI for two years?

For annual compounding, CI − SI = P × R²/10,000. For ₹10,000 at 10% for 2 years, the difference is ₹100.

How do you calculate simple interest for a period given in months?

Convert months into years using T = months/12. For example, 6 months is 1/2 year.

Which is greater for the same principal, rate and time: SI or CI?

For a period longer than one compounding period, CI is greater because it includes interest on earlier interest. For exactly one period, SI and CI are equal.

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