Hello, and welcome to today's mathematics lesson. Today, we are diving into Chapter Eleven: Simple Interest. By the end of this session, you will understand exactly what simple interest means, how to calculate it, and how to solve problems involving principal, rate, time, and amount.
Let us begin with the fundamental terms you need to know.
First, Simple Interest. This is the extra money that a lender receives from a borrower, as compensation for the money that was borrowed. The terms S.I. and I mean exactly the same thing.
Next, the Principal, denoted by P. This is the original sum of money that the lender gives to the borrower. Think of it as the starting amount.
Then we have the Rate of Interest, denoted by R. This is the interest earned on every hundred rupees for a fixed period. For example, if the rate is eighteen percent per year, that means on one hundred rupees, the interest for one year is eighteen rupees. Similarly, if the rate is one point five percent per month, the interest for one month on one hundred rupees is one rupee and fifty paise.
The Time Period, denoted by T, is simply the duration for which the principal is borrowed or lent.
Finally, the Amount, denoted by A. This is the total sum that the borrower returns to the lender. It includes both the original principal and the interest earned. So, A = P + I.
Now, here comes the heart of this chapter: the formula for simple interest.
The interest is calculated as: I = (P × R × T) / 100.
This single formula connects all four quantities: principal, rate, time, and interest. From this, we can also derive three other useful formulas.
To find the principal when you know the interest: P = (I × 100) / (R × T).
To find the rate: R = (I × 100) / (P × T).
And to find the time: T = (I × 100) / (P × R).
Let us see how this works with a practical example.
Suppose you borrow three thousand rupees at four percent per year for five years. Using our formula, the interest equals three thousand multiplied by four, multiplied by five, divided by one hundred. That gives six hundred rupees. Therefore, the amount you must repay is three thousand plus six hundred, which equals three thousand six hundred rupees.
Here is a crucial point to remember about units.
The time period must always match the rate period. If the rate is given per year, time must be in years. If the rate is given per month, time must be in months.
For instance, if you calculate interest on eight hundred rupees at six percent per month for nine months, you use nine directly as the time. The interest becomes eight hundred multiplied by six, multiplied by nine, divided by one hundred, giving four hundred thirty-two rupees.
Sometimes, you need to calculate time when dates are given.
Here is the rule: the starting date is not included, but the ending date is included.
Imagine money lent on August tenth and returned on October twenty-second of the same year. From August, you count twenty-one days, not thirty-one, because you exclude August tenth. Add all of September, which is thirty days. Then add twenty-two days from October. Total: seventy-three days.
Since the rate is per annum, convert days to years: seventy-three divided by three hundred sixty-five, which simplifies to one-fifth of a year. Now apply the formula with principal nine hundred rupees, rate thirty-five over four percent, and time one-fifth year. The simple interest works out to fifteen rupees and seventy-five paise.
Let us explore how to find any missing quantity when the others are known.
Suppose you want to find what principal earns four hundred eighty rupees interest in three years at sixteen percent per year. Rearranging our formula, principal equals interest multiplied by one hundred, divided by rate multiplied by time. So, four hundred eighty multiplied by one hundred, divided by sixteen multiplied by three. This gives one thousand rupees.
Or, consider finding the time needed for two thousand one hundred rupees to earn five hundred twenty-five rupees interest at five percent per annum. Time equals five hundred twenty-five multiplied by one hundred, divided by two thousand one hundred multiplied by five. The answer is five years.
Here is an interesting challenge: at what rate will a sum double itself in ten years? If principal is one hundred, amount becomes two hundred, so interest is one hundred. Rate equals one hundred multiplied by one hundred, divided by one hundred multiplied by ten, giving ten percent per annum.
When problems give you the amount directly, remember this relationship: A = P + I.
Suppose you need to find what principal grows to nine hundred ninety-two rupees at four percent in six years. On one hundred rupees, the interest for six years at four percent would be twenty-four rupees. So the amount becomes one hundred twenty-four rupees. By unitary method, when amount is one hundred twenty-four, principal is one hundred. Therefore, when amount is nine hundred ninety-two, principal equals one hundred divided by one hundred twenty-four, multiplied by nine hundred ninety-two, which is eight hundred rupees.
Alternatively, using algebra: nine hundred ninety-two equals P plus (P × R × T) / 100. This becomes nine hundred ninety-two equals P multiplied by one hundred twenty-four, divided by one hundred. Solving, P equals eight hundred rupees.
Consider this: how long will one thousand five hundred rupees take to become two thousand forty rupees at eight percent per annum?
First, find the interest: two thousand forty minus one thousand five hundred equals five hundred forty rupees. Then, time equals five hundred forty multiplied by one hundred, divided by one thousand five hundred multiplied by eight. This simplifies to four and a half years, or four years and six months.
Here is a comparison problem.
Person A invests eight thousand rupees, and person B invests eleven thousand rupees, both at the same rate for three years. Person B receives seven hundred twenty rupees more interest than A. Find the rate.
Interest for A equals eight thousand multiplied by R multiplied by three, divided by one hundred, which is two hundred forty R. Interest for B equals eleven thousand multiplied by R multiplied by three, divided by one hundred, which is three hundred thirty R. The difference is ninety R, which equals seven hundred twenty. Therefore, R equals eight percent.
Notice that B invested three thousand rupees more than A. The extra interest of seven hundred twenty rupees comes solely from this difference. So, three thousand multiplied by R multiplied by three, divided by one hundred, equals seven hundred twenty. This also gives R equals eight percent.
Finally, here is an elegant problem involving fractions.
A sum becomes seven-fifths of itself in four years. Find the rate.
Let principal be x. Then amount is seven x over five. Interest equals seven x over five minus x, which is two x over five. Rate equals one hundred multiplied by two x over five, divided by x multiplied by four. The x cancels, and you get forty divided by four, which is ten percent.
Using numbers instead: let principal be one hundred. Amount becomes one hundred forty. Interest is forty. Rate equals one hundred multiplied by forty, divided by one hundred multiplied by four, giving ten percent.
Let us recap the key takeaways from today's lesson.
First, simple interest is the extra money paid for using borrowed money. Second, the four essential quantities are principal, rate, time, and interest, connected by the formula I = (P × R × T) / 100. Third, amount always equals principal plus interest. Fourth, time units must match the rate units, years with yearly rates, months with monthly rates. Fifth, when calculating time from dates, exclude the start date but include the end date. Sixth, any one of the four quantities can be found if the other three are known, by rearranging the formula.
Simple interest is everywhere in daily life, from bank deposits to loans to investments. Mastering these calculations gives you a powerful tool for understanding money and making informed decisions. Keep practicing, stay curious, and I look forward to seeing you in the next lesson.