Simple Interest vs Compound Interest Formulas
| Aspect |
Simple Interest (SI) |
Compound Interest (CI) |
| Basic Formula |
SI = (P × R × T) / 100 |
CI = P[(1 + R/100)^n – 1] |
| Amount Formula |
A = P(1 + RT/100) |
A = P(1 + R/100)^n |
| Interest Calculation |
Calculated only on principal |
Calculated on principal + accumulated interest |
| Growth Pattern |
Linear growth |
Exponential growth |
| Time Variable |
T = Time in years |
n = Number of compounding periods |
| When to Use |
Short-term loans, simple calculations |
Long-term investments, savings accounts |
Compound Interest Formulas (Extended)
| Formula Type |
Formula |
Variables |
When Used |
| Annual Compounding |
A = P(1 + R/100)^n |
n = number of years |
Interest compounded once per year |
| Semi-Annual Compounding |
A = P(1 + R/200)^(2n) |
Compounded twice yearly |
Interest added every 6 months |
| Quarterly Compounding |
A = P(1 + R/400)^(4n) |
Compounded 4 times yearly |
Interest added every 3 months |
| Monthly Compounding |
A = P(1 + R/1200)^(12n) |
Compounded 12 times yearly |
Interest added monthly |
| General Compounding |
A = P(1 + R/(100k))^(kn) |
k = compounding frequency |
For any compounding frequency |
| Compound Interest |
CI = A – P |
CI = Compound Interest |
Finds only the interest component |
Differences: Simple Interest vs Compound Interest
| Parameter |
Simple Interest |
Compound Interest |
| Definition |
Interest on principal only |
Interest on principal + interest |
| Formula Complexity |
Simple, linear |
Exponential, more complex |
| Interest Amount |
Same every period |
Increases every period |
| Total Returns |
Lower |
Higher |
| Calculation Difficulty |
Easy |
Moderately difficult |
| Real-world Use |
Personal loans, car loans |
Savings accounts, investments, mortgages |
| Time Impact |
Proportional increase |
Exponential increase |
सरल ब्याज सूत्र (Simple Interest Formula in Hindi)
| सूत्र का नाम |
सूत्र |
चर (Variables) |
| सरल ब्याज |
साधारण ब्याज = (मूलधन × दर × समय) / 100 |
मूलधन (P) = Principal
दर (R) = Rate
समय (T) = Time |
| कुल राशि |
कुल राशि = मूलधन + साधारण ब्याज |
A = Amount |
| मूलधन |
मूलधन = (ब्याज × 100) / (दर × समय) |
P = Principal |
| ब्याज दर |
दर = (ब्याज × 100) / (मूलधन × समय) |
R = Rate |
| समय |
समय = (ब्याज × 100) / (मूलधन × दर) |
T = Time |
उदाहरण (Example): यदि ₹10,000 की राशि 5% वार्षिक दर से 2 वर्षों के लिए उधार ली जाती है:
- मूलधन (P) = ₹10,000
- दर (R) = 5%
- समय (T) = 2 वर्ष
- साधारण ब्याज = (10,000 × 5 × 2) / 100 = ₹1,000
- कुल राशि = ₹10,000 + ₹1,000 = ₹11,000
Practical Examples with Step-by-Step Solutions
Example 1: Finding Simple Interest
Question: Calculate the simple interest on ₹5,000 at 8% per annum for 3 years.
Solution:
- P = ₹5,000
- R = 8%
- T = 3 years
- SI = (5,000 × 8 × 3) / 100 = ₹1,200
Example 2: Finding Total Amount
Question: What amount will ₹8,000 become in 4 years at 6% simple interest?
Solution:
- A = P(1 + RT/100)
- A = 8,000(1 + (6 × 4)/100)
- A = 8,000(1 + 0.24)
- A = ₹9,920
Example 3: Finding Rate
Question: At what rate percent per annum will ₹2,000 amount to ₹2,400 in 4 years?
Solution:
- R = [(A/P) – 1] × (100/T)
- R = [(2,400/2,000) – 1] × (100/4)
- R = [1.2 – 1] × 25
- R = 5%
Frequently Asked Questions about Simple Interest Formula
Q. What is the simple interest formula and how is it different from compound interest?
The simple interest formula is SI = (P × R × T) / 100, where interest is calculated only on the principal amount. Compound interest uses CI = P[(1 + R/100)^n – 1], where interest is calculated on both principal and accumulated interest. Simple interest grows linearly, while compound interest grows exponentially, making compound interest yield higher returns over time.
Q. How do you calculate the total amount using simple interest?
The total amount (A) is calculated using the formula A = P + SI or A = P(1 + RT/100), where P is the principal, R is the rate of interest, and T is time. First, calculate the simple interest using SI = (P × R × T) / 100, then add it to the principal to get the total amount.
Q. What is the formula to find the principal amount when simple interest is given?
The principal formula is P = (SI × 100) / (R × T), where SI is simple interest, R is the rate, and T is time. Alternatively, if the total amount is known, use P = A / (1 + RT/100). This formula is useful when you need to determine the initial investment or loan amount.
Q. How can I convert time periods (months/days) to years in simple interest calculations?
Convert months to years by dividing by 12 (e.g., 6 months = 6/12 = 0.5 years). Convert days to years by dividing by 365 (e.g., 73 days = 73/365 = 0.2 years). Always ensure time is in years when using the standard simple interest formula, unless the rate is also adjusted to match the time period.
Q. Which is better for savings: simple interest or compound interest?
Compound interest is significantly better for savings and long-term investments because interest earns additional interest, creating exponential growth. For example, ₹10,000 at 10% for 5 years yields ₹5,000 in simple interest but ₹6,105 in compound interest (annual compounding). However, for borrowers, simple interest loans are more favorable as they cost less.
Q. How do you calculate simple interest for different compounding frequencies?
Simple interest doesn’t use compounding frequencies—it always calculates interest on the principal only. Compound interest varies by frequency: annually (n=1), semi-annually (n=2), quarterly (n=4), or monthly (n=12). Use A = P(1 + R/(100k))^(kn), where k is the compounding frequency per year.
Q. What is the formula to find the rate of interest when principal, time, and interest are given?
The rate formula is R = (SI × 100) / (P × T), where SI is simple interest, P is principal, and T is time in years. If you know the total amount instead, use R = [(A/P) – 1] × (100/T). Express the rate as a percentage per annum.
Q. Can simple interest ever exceed compound interest?
No, compound interest always equals or exceeds simple interest for the same principal, rate, and time period (when time ≥ 1 compounding period). They’re equal only for exactly one compounding period. As time increases, compound interest grows exponentially larger than simple interest due to the effect of interest-on-interest.
Q. How do you solve problems where the rate or time is given in different units?
Always convert to consistent units. If rate is per month, convert to per annum by multiplying by 12. If time is in months, divide by 12 to get years. For quarterly rates, multiply by 4 for annual rate. The standard formula assumes annual rate and time in years, so adjust accordingly before calculating.
Q. What are real-world applications where simple interest is commonly used?
Simple interest is used in:
- Personal loans and car loans (many short-term loans)
- Certificate deposits in some banks
- Short-term business loans (90-180 days)
- Promissory notes and bonds
- Legal judgments for calculating owed amounts
- Installment purchases where interest is calculated upfront
Banks increasingly use compound interest for deposits, but simple interest remains common for straightforward lending scenarios.
Important Tips for Students
- Always identify what’s given (P, R, T, SI, or A) before selecting the formula
- Check units: Ensure time is in years and rate is per annum
- Practice conversions: Master converting months/days to years
- Understand the context: Know when to use simple vs. compound interest
- Verify answers: Check if your calculated values make logical sense
- Show work: Write all steps clearly for better understanding and marks
