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Imagine you borrow some money from your friend, or from a bank. When you return that money, you usually have to pay back a little extra. This extra money is called 'interest'! Simple Interest is the easiest way to calculate this extra money, where you only pay interest on the original amount you borrowed. It's super important for understanding loans, savings, and many competitive exam questions.
When you need to find the Simple Interest, just think of R × T as a combined percentage. Calculate this percentage of the Principal (P). This saves you from dividing by 100 separately and simplifies mental math!
If money becomes 'N' times (like double means N=2, triple means N=3) in 'T' years at simple interest, the rate 'R' can be found quickly. The interest earned is (N-1) times the principal. So, the trick is R = ((N-1) × 100) / T. Similarly, if you know R, you can find T with T = ((N-1) × 100) / R.
Sometimes, a sum is divided into two parts and lent at different rates for the same time, giving the same simple interest. If P1 and P2 are the parts, and R1 and R2 are rates, and T is same, then P1 × R1 = P2 × R2. This helps find parts easily.
If the time is given in months or days, convert it to years before applying the formula. For months, divide by 12. For days, divide by 365 (or 366 for a leap year, though usually 365). This is a common mistake point, so remember to adjust Time!
Let's start with a simple idea. When you lend money to someone, or a bank lends money to you, they don't just ask for the same amount back. They ask for a little extra. This extra money is the 'rent' for using their money, and we call it interest. Simple Interest is the most basic way to calculate this rent. It means the interest is always calculated only on the original amount you borrowed or lent, called the Principal.
Let's say your friend, Rahul, needs ₹1,000 for 2 years. You lend him the money and say, "Rahul, you have to pay me back with 10% simple interest per year."
Here:
Using the formula SI = (P × R × T) / 100:
SI = (1000 × 10 × 2) / 100
SI = (20000) / 100
SI = ₹200
So, Rahul has to pay you ₹200 extra. The total amount Rahul will pay back to you will be:
Amount = Principal + Simple Interest
Amount = 1000 + 200
Amount = ₹1,200
Notice that for Simple Interest, the interest is always on the initial ₹1,000. Even in the second year, the interest is calculated on ₹1,000, not on ₹1,100 (1000 + 100 from first year's interest). This makes it 'simple'!
Simple Interest (साधारण ब्याज)
SI = (P × R × T) / 100Amount (मिश्रधन)
Amount = Principal + Simple Interest (A = P + SI)Principal (मूलधन)
P = (SI × 100) / (R × T)Rate (दर)
R = (SI × 100) / (P × T)Time (समय)
T = (SI × 100) / (P × R)| Year | Principal (₹) | Interest for the Year (₹) | Total Simple Interest (₹) | Total Amount (₹) |
|---|---|---|---|---|
| 1 | 10,000 | 500 | 500 | 10,500 |
| 2 | 10,000 | 500 | 1,000 | 11,000 |
| 3 | 10,000 | 500 | 1,500 | 11,500 |
| 4 | 10,000 | 500 | 2,000 | 12,000 |
Q: A person invested ₹8,000 in a fixed deposit for 3 years at a simple interest rate of 6% per annum. What will be the simple interest earned?
Q: What amount will a person get back if they lent ₹12,000 to a friend for 2 years at 5% simple interest per annum?
Q: A sum of money doubles itself in 8 years at a certain rate of simple interest. Find the annual rate of interest.
Q: If ₹15,000 gives an interest of ₹2,700 in 3 years, what is the annual rate of simple interest?
You want to save money for a new bicycle. You put ₹5,000 in a savings account that gives 4% simple interest every year. How much extra money will you earn in 2 years?
Your friend needs ₹2,000 for 1 year and promises to pay you back with 5% simple interest. How much total money will your friend return to you?
Your uncle took a small home loan of ₹1,00,000 at 10% simple interest per year for 3 years. How much total interest will he pay over these 3 years?
You invested ₹10,000 in a scheme that promises to double your money in 5 years at simple interest. What is the annual rate of interest offered by the scheme?
A certain sum of money at simple interest amounts to ₹13,500 in 5 years and to ₹16,200 in 8 years. The sum (principal) is:
At what rate per annum will a sum of money triple itself in 10 years at simple interest?
A sum was invested for 4 years at 8% simple interest per annum. If the interest earned was ₹1,600, what was the principal sum?
In how many years will ₹4,000 yield a simple interest of ₹1,200 at an annual interest rate of 5%?
1Calculate the Simple Interest on ₹6,000 at 5% per annum for 4 years.
2What is the total amount to be paid if ₹15,000 is borrowed at 8% simple interest for 2 years?
3A sum of money fetches ₹2,400 as simple interest at 10% per annum in 3 years. What is the principal amount?
4In what time will ₹5,000 earn ₹1,500 as simple interest at 6% per annum?
5At what annual rate of simple interest will ₹10,000 amount to ₹12,500 in 5 years?
6If the simple interest on a certain sum at 12% per annum for 3 years is ₹2,700, what is the sum?
7A sum of money doubles itself in 10 years at simple interest. The rate of interest per annum is:
8What is the simple interest on ₹20,000 for 9 months at 10% per annum?
9A sum of ₹800 amounts to ₹920 in 3 years at simple interest. If the rate of interest is increased by 3%, what will be the new amount?
10A person invested two equal amounts in two different schemes. The first scheme gives 6% simple interest and the second gives 8% simple interest. If the total simple interest after 5 years is ₹3,500, what was the amount invested in each scheme?
When you need to find the Simple Interest, just think of R × T as a combined percentage. Calculate this percentage of the Principal (P). This saves you from dividing by 100 separately and simplifies mental math!
If money becomes 'N' times (like double means N=2, triple means N=3) in 'T' years at simple interest, the rate 'R' can be found quickly. The interest earned is (N-1) times the principal. So, the trick is R = ((N-1) × 100) / T. Similarly, if you know R, you can find T with T = ((N-1) × 100) / R.
Sometimes, a sum is divided into two parts and lent at different rates for the same time, giving the same simple interest. If P1 and P2 are the parts, and R1 and R2 are rates, and T is same, then P1 × R1 = P2 × R2. This helps find parts easily.
If the time is given in months or days, convert it to years before applying the formula. For months, divide by 12. For days, divide by 365 (or 366 for a leap year, though usually 365). This is a common mistake point, so remember to adjust Time!
SI = (P × R × T) / 100Amount = Principal + Simple Interest (A = P + SI)P = (SI × 100) / (R × T)+2 more formulas below