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Have you ever wondered how banks calculate the interest you earn on a savings account or the extra money you pay when you borrow money? This extra amount is called interest. When the interest is calculated only on the original amount of money lent or borrowed, and not on any previously earned interest, it is called simple interest.
Simple interest is widely used in banking, loans, investments, and daily financial dealings because it is easy to understand and calculate. In this chapter, you will learn what simple interest is, its key components, how to calculate it, and how it applies to real-life financial situations.
Before we dive into formulas and calculations, let's first understand the fundamental parts of simple interest:
The interest earned or paid depends on these three components. The more money you invest (principal), the higher the interest. Similarly, the longer the time period or the greater the rate of interest, the more interest you get or pay.
After understanding the components, we now look at the formula to calculate simple interest. The simple interest is directly proportional to the principal, rate, and time. This relationship is given by the formula:
Simple Interest Formula:
\[ SI = \frac{P \times R \times T}{100} \]
| Variable | Meaning | Units/Example |
|---|---|---|
| P | Principal (original amount) | INR (e.g., Rs. 10,000) |
| R | Rate of Interest (per annum) | Percentage (%) (e.g., 5%) |
| T | Time Period | Years (e.g., 2 years) |
| SI | Simple Interest | INR (calculated interest) |
Why divide by 100? Because the rate is given as a percentage, and percentages mean "per 100". To convert percentage to a decimal fraction used in multiplication, we divide by 100.
Step 1: Identify the given values: \(P = 10000\), \(R = 5\%\), \(T = 1\) year.
Step 2: Substitute these values into the formula:
\[ SI = \frac{P \times R \times T}{100} = \frac{10000 \times 5 \times 1}{100} = \frac{50000}{100} = 500 \]
Answer: The simple interest earned in 1 year is Rs. 500.
Step 1: Given \(SI = 1200\), \(R = 6\%\), \(T = 2\) years.
Step 2: Rearrange the simple interest formula to find principal \(P\):
\[ P = \frac{SI \times 100}{R \times T} \]
Step 3: Substitute the values:
\[ P = \frac{1200 \times 100}{6 \times 2} = \frac{120000}{12} = 10000 \]
Answer: The principal amount is Rs. 10,000.
Step 1: Convert 9 months to years: \(T = \frac{9}{12} = 0.75\) years.
Step 2: Identify other values: \(P = 8000\), \(R = 7.5\%\).
Step 3: Use the formula:
\[ SI = \frac{8000 \times 7.5 \times 0.75}{100} = \frac{45000}{100} = 450 \]
Answer: The simple interest for 9 months is Rs. 450.
Step 1: Convert 6 months into years: \(T = \frac{6}{12} = 0.5\) years.
Step 2: Calculate the interest (discount):
\[ SI = \frac{5000 \times 4 \times 0.5}{100} = \frac{10000}{100} = 100 \]
Step 3: The amount saved by the borrower, or the discount, is Rs. 100.
Answer: The borrower saves Rs. 100 by getting the loan discounted for 6 months.
Step 1: Calculate interest for the first year:
\[ SI_1 = \frac{12000 \times 6 \times 1}{100} = 720 \]
Step 2: Calculate interest for the next two years:
\[ SI_2 = \frac{12000 \times 7 \times 2}{100} = \frac{168000}{100} = 1680 \]
Step 3: Add both interests to find total interest:
\[ SI_{total} = SI_1 + SI_2 = 720 + 1680 = 2400 \]
Answer: The total interest earned over 3 years is Rs. 2,400.
When to use: When time period is given as a fraction of a year to prevent calculation errors.
When to use: To rapidly find interest for 1 year without complex calculations.
When to use: When dealing with problems involving changing time periods or rates.
When to use: In word problems involving loans or investments to keep amounts distinct.
When to use: When any one of P, R, or T is unknown and you have the other variables.
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