Simple and Compound Interest for the Assam Police Constable Exam
Simple and compound interest is the chapter that connects the mathematics of the examination with the arithmetic of everyday money. In the SLPRB Assam Police Constable (AB & UB) paper the questions are usually of one or two lines, but they test whether the candidate understands the difference between interest that is paid only on the original sum and interest that is paid on interest as well. Simple interest grows in a straight line, because the same amount is added every year. Compound interest grows faster, because each year's interest is added to the principal and then earns interest in the following year. The whole chapter is an application of percentage, so a candidate who is comfortable with the percentage chapter will find that the formulas here are easy to remember and easy to use. The method followed here is the one from the Master Book: Maths Masti (D. Hurina), which writes the principal, the rate and the time in a fixed order and then substitutes without rushing, because the commonest mistakes in this chapter come from using the wrong time, from forgetting to convert the rate to its decimal form, or from confusing the amount with the interest.
Why Interest Questions Appear in the Assam Police Paper
The topic is useful in an objective paper because it has a small number of fixed formulas and produces clean answers. It also tests the candidate's care with units, since the rate is given per year but the time may be given in months, and a small slip there changes the answer completely. Questions on a bank deposit, a loan, a scheme that doubles a sum, or the growth of a population all use the same ideas, so one well-practised method serves several question types.
Terms You Should Know
- Principal: the sum of money borrowed or invested.
- Rate: the interest for one hundred units of money for one year.
- Time: the period for which the money is kept, usually in years.
- Interest: the extra money earned or paid for the use of the principal.
- Amount: the principal together with the interest.
- Compounded annually: interest added to the principal once every year.
- Accumulated amount: the amount after compound interest has been added.
It is important to keep the two words apart: the interest is the extra sum, while the amount is the principal plus the interest. Many questions ask for one when the candidate has calculated the other, and writing both down prevents the error.
Simple Interest and Its Four Quantities
Simple interest equals the principal multiplied by the rate multiplied by the time, divided by one hundred. There are four quantities in the formula, the principal, the rate, the time and the interest, and any one of them can be found when the other three are known. The interest is the same every year, so the interest for two years is twice the interest for one year, and the interest for six months is half the yearly interest. The straight-line growth of simple interest is what makes it so easy to work with.
Finding Principal, Rate and Time by Rearrangement
The principal equals the interest multiplied by one hundred, divided by the rate multiplied by the time. The rate equals the interest multiplied by one hundred, divided by the principal multiplied by the time. The time equals the interest multiplied by one hundred, divided by the principal multiplied by the rate. When the time is given in months, convert it into years by dividing by twelve, and when it is given in days, divide by three hundred and sixty-five, unless the question specifies three hundred and sixty. Writing the formula first and then placing the known quantities in their correct positions is the safest route.
Compound Interest and the Yearly Multiplication
Compound interest is found by multiplying the principal by one plus the rate, raised to the power of the number of years, to obtain the amount, and then subtracting the principal to obtain the interest. Because the interest of each year is added to the principal, the amount grows faster than with simple interest. For two years the amount is the principal multiplied by one plus the rate, and then again by one plus the rate, so the factor is applied twice. When the time is short and the rate is small, the extra growth over simple interest is also small, but it grows quickly as the time increases.
The Difference Between Simple and Compound Interest
For the first year, simple interest and compound interest are equal, because there is no previously added interest to earn interest. The difference appears from the second year onwards. For two years, the difference between compound interest and simple interest is the simple interest on the first year's interest, which equals the principal multiplied by the square of the rate, divided by the square of one hundred. A standard question asks for this difference, and the result is worth remembering because it appears in many papers.
Half-Yearly and Quarterly Compounding
When interest is compounded half-yearly, the rate for each period is half the yearly rate and the number of periods is twice the number of years. When it is compounded quarterly, the rate for each period is a quarter of the yearly rate and the number of periods is four times the number of years. The same formula is used, with the adjusted rate and the adjusted number of periods. This adjustment is a favourite trap, and a question that asks for half-yearly compounding is testing whether the candidate remembers to change both the rate and the time.
Growth, Population and Depreciation Problems
The same formula describes the growth of a population and the increase in the value of an asset, because both change by a fixed percentage each year. For depreciation, the value falls by a fixed percentage each year, so the multiplying factor is one minus the rate instead of one plus the rate. A question on the population of a town, the value of a machine, or the price of an article over several years is solved in exactly the same way as a compound interest question.
Installments and Other Practical Questions
Some questions ask how much a sum becomes when it is lent in two parts at different rates, or how a total interest is shared between two parts of a principal. These are solved by taking the unknown part as a symbol, writing the interest on each part separately, and adding to match the given total. Installment questions, where a loan is repaid in equal yearly amounts, can be solved by working from the last payment backwards, but such questions are rare in the Assam Police paper and are best attempted only if the simpler forms are secure.
Shortcut Techniques for the Exam Hall
Write the principal, rate and time in a fixed order before substituting, and convert the rate into a decimal at once. For compound interest over two years, remember that the total percentage increase is the sum of the yearly rate and its half-square, which is a quick check on the answer. Use the standard formula for the two-year difference between the two types of interest. When the time is in months, convert it to years before doing anything else. Since compound interest is a percentage application, use the multiplying-factor method of the percentage chapter instead of repeating long multiplication.
Common Traps and Errors
- Confusing the amount with the interest, and reporting one when the other is asked.
- Using a time in months as if it were a time in years.
- Forgetting to halve the rate and double the periods for half-yearly compounding.
- Using one plus the rate for depreciation instead of one minus the rate.
- Adding the yearly rates for compound interest instead of multiplying the factors.
- Writing the rate as a whole number instead of dividing by one hundred.
A Study Plan for This Chapter
- Learn the simple interest formula and its three rearrangements.
- Practise converting time from months and days into years.
- Learn the compound interest formula and the yearly step method.
- Work on the two-year difference and on half-yearly and quarterly compounding.
- Finish with growth and depreciation problems, and revise the amount and the interest each week.
Frequently Asked Questions
What is the difference between simple and compound interest?
In simple interest the same amount is added every year, calculated on the original principal. In compound interest the interest is added to the principal each year, so the following year earns interest on the interest as well, and the amount grows faster.
Are simple and compound interest equal in the first year?
Yes. In the first year there is no previously added interest, so both are calculated on the same principal and are equal. The difference begins from the second year.
How do I handle half-yearly compounding?
Halve the yearly rate to get the rate for each period, and double the number of years to get the number of periods, then use the same compound interest formula. For quarterly compounding, take a quarter of the rate and four times the number of periods.
What is the two-year difference between compound and simple interest?
For two years the difference equals the principal multiplied by the square of the rate divided by the square of one hundred. It is simply the simple interest on the first year's interest.
How is depreciation different from compound interest?
Depreciation is a fixed percentage fall each year, so the multiplying factor is one minus the rate, while compound interest uses one plus the rate. Apart from this change of sign the method is identical.