How to prepare Simple Interest and Compound Interest for AFCAT?

If you are preparing for the AFCAT exam, you might be wondering how to tackle the numerical ability section, especially the questions on simple interest and compound interest. These topics are important as they test your basic mathematical skills and your ability to apply formulas and concepts in different situations.

In this article, we will provide you with some tips and tricks on how to prepare simple interest and compound interest for AFCAT exam. We will also provide you with some practice questions and mock tests that you can use to check your progress and improve your speed and accuracy.

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What is Simple Interest and Compound Interest?

Simple interest is the interest calculated on the principal amount only. The formula for simple interest is:

Simple Interest = (Principal x Rate x Time) / 100

Compound interest is the interest calculated on the principal amount as well as the accumulated interest. The formula for compound interest is:

Compound Interest = Principal x (1 + Rate/100)^Time – Principal

You should memorize these formulas and learn how to apply them in different scenarios. For example, you should know how to find the amount, rate or time given the other two variables. You should also know how to compare simple interest and compound interest for different periods and rates.

How to Solve Simple Interest and Compound Interest Questions for AFCAT exam?

To solve simple interest and compound interest questions for AFCAT exam, you should follow these steps:

• Read the question carefully and identify the given data and the required data.
• Choose the appropriate formula based on whether it is simple interest or compound interest.
• Substitute the given values in the formula and simplify it to find the unknown value.
• Check your answer by plugging it back in the formula or by using another method.
• If possible, use shortcuts or tricks to save time and avoid calculations.

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Some of the shortcuts or tricks that you can use are:

• To find the simple interest for two years at a certain rate, double the rate and multiply it with the principal. For example, if the principal is Rs. 1000 and the rate is 10%, then the simple interest for two years is Rs. 1000 x 2 x 10% = Rs. 200.
• To find the compound interest for two years at a certain rate, square the rate and add it to twice the rate. Then multiply it with the principal. For example, if the principal is Rs. 1000 and the rate is 10%, then the compound interest for two years is Rs. 1000 x (10^2 + 2 x 10)% / 100 = Rs. 210.
• To find the difference between simple interest and compound interest for two years at a certain rate, multiply the principal with the square of half of the rate. For example, if the principal is Rs. 1000 and the rate is 10%, then the difference between simple interest and compound interest for two years is Rs. 1000 x (10/2)^2 / 100 = Rs. 25.

How to Practice Simple Interest and Compound Interest Questions for AFCAT exam?

To practice simple interest and compound interest questions for AFCAT exam, you should use a variety of sources such as books, online platforms, mock tests, etc. You should also solve different types of questions such as word problems, data interpretation, missing data, etc.

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Simple Interest Questions for Practice

Question 1: Given that simple interest on a certain sum of money is Rs. 4016.25 at 9% per annum in 5 years. Find the sum of money.

Solution: Let P be the principal amount or sum of money. Time (T) = 5 years, Rate of interest ® = 9%, Simple interest earned (SI) = Rs. 4016.25. As we know, SI = PTR/100, Rs. 4016.25 = (P × 5 × 9)/100, P = (Rs. 4016.25 × 100)/ (5 × 9) = Rs. 8925. Therefore, the sum of money is Rs. 89251.

Question 2: Calculate the simple interest on Rs. 8000 for 15 months at 6 paise per rupee per month.

Solution: Given, Principal amount (P) = Rs. 8000, Time (T) = 15 months, Rate ® = 6 paise per rupee per month. Here, the rate of interest and the time are given per month. So, we can use the simple interest formula as: SI = PTR/100 = (Rs. 8000 × 15 × 6)/100 = Rs. 7200. Therefore, the simple interest is Rs. 72001.

Question 3: A sum of Rs. 25000 will become Rs. 31000 in 48 months at some rate of simple interest. Find the rate of interest per annum.

Solution: Given, Principal amount (P) = Rs. 25000, Time (T) = 48 months = (48/12) years = 4 years, Total amount after 4 years (A) = Rs. 31000, Let R be the rate of interest. As we know, A = P + SI, Rs. 31000 = Rs. 25000 + [ (Rs. 25000 × 4 × R)/100], Rs. 31000 – Rs. 25000 = Rs. 1000 × R, R = Rs. 6000/Rs. 1000 = 6 Therefore, the rate of interest per annum is 6%1.

Question 4: A sum of Rs.12000 is lent out at a rate of 5% per annum simple interest for 5 years. What will be the amount after 5 years?

Solution: Given, Principal amount (P) = Rs.12000, Rate of interest per annum ® = 5%, Time (T) = 5 years, SI=PTR/100=(Rs12000×5×5)/100=Rs3000 Thus, the total amount after 5 years=P+SI=Rs12000+Rs3000=Rs150001.

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Question 5: A sum of Rs1750 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. What is the interest accumulated on each part?

Solution: Given, Principal (P) = Rs1750 Let x be the first part of the sum so that the second part will be (Rs1750–x). We know that SI=PTR/1001.

Compound Interest Questions for Practice

Question 1: Find the compound interest (CI) on Rs. 12,600 for 2 years at 10% per annum compounded annually.

Solution: Given, Principal (P) = Rs. 12,600, Rate ® = 10%, Number of years (n) = 2. Using the formula for compound interest, A = P [1 + (R/100)]n = 12600 [1 + (10/100)]2 = 12600 [1 + (1/10)]2 = 12600 [ (10 + 1)/10]2 = 12600 × (11/10) × (11/10) = 126 × 121 = 15246. Total amount, A = Rs. 15,246. Compound interest (CI) = A – P = Rs. 15,246 – Rs. 12,600 = Rs. 26461.

Question 2: At what rate of compound interest per annum, a sum of Rs. 1200 becomes Rs. 1348.32 in 2 years?

Solution: Let R% be the rate of interest per annum. Given, Principal (P) = Rs. 1200, Total amount after 2 years (A) = Rs. 1348.32, n = 2. We know that, A = P [1 + (R/100)]n. Rs. 1348.32 = Rs. 1200 [1 + (R/100)]2. Dividing both sides by Rs.1200 we get: [1 + (R/100)]2 = 134832/120000 or [1 + (R/100)]2 = 2809/2500 or [1 + (R/100)]2 = (53/50)2. Taking square root on both sides we get: [1 + (R/100)] = √(53/50)2 or [1 + (R/100)] =53/50 or R/100=53/50-1 or R=300/50=6%. Hence, the rate of interest is 6%1.

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Question 3: A TV was bought for Rs. 21,000. The value of the TV was depreciated by 5% per annum1. Find the value of the TV after 3 years.

Solution: Given, Principal amount (P) = Rs.21,000, Rate of depreciation®=5%, Time(n)=3 years. Using the formula of CI for depreciation: A=P[1-(R/100)]n. Substituting the values we get: A=Rs21,000[1-(5/100)]3. Solving this we get: A=Rs18,004.875. Therefore, the value of the TV after 3 years is Rs18,004.8751.

Question 4: Find the compound interest on Rs48,000 for one year at 8% per annum when compounded half-yearly.

Solution: Given, Principal amount(P)=Rs48,000, Rate®=8% p.a., Time(n)=1 year. Also given that the interest is compounded half-yearly. So using the formula for half-yearly compounding: A=P[1+(R/(200))]^(2n). Substituting the values we get: A=Rs48,000[1+(8/(200))]^(2×1). Solving this we get: A=Rs51,840. Therefore the compound interest is: CI=A-P=Rs51,840-Rs48,000=Rs3,8401.

Question 5: Find the compound interest on Rs8000 for one year at 4% per annum when compounded quarterly.

Solution: Given Principal amount(P)=Rs8000, Rate®=4% p.a., Time(n)=1 year. Also given that the interest is compounded quarterly. So using the formula for quarterly compounding: A=P[1+(R/(400))]^(4n). Substituting the values we get: A=Rs8000[1+(4/(400))]^(4×1). Solving this we get: A=Rs8326. Therefore the compound interest is: CI=A-P=Rs8326-Rs8000=Rs3261.

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We hope that this article has helped you understand how to prepare simple interest and compound interest for AFCAT exam. Remember to practice regularly, revise your formulas, use shortcuts and tricks, and take mock tests to ace this section. All the best for your exam!