We have all learnt how to calculate simple interest and compound interest in school. In this chapter, I will not emphasize too much on the basics; instead I will focus solely on some ‘secret short- cut methods’ that will help you save time in your competitive exams.
Let us begin with simple interest.
For ‘Principal’ amount we will use the letter (P) For ‘Time’ we will use (T)
For ‘Rate of Interest’ we will use the letter (R)
We all know that the formula for simple interest is:
Let us solve a basic questions as a warm-up
Q1) What is the Simple Interest on `1000 for 5 years at the rate of 8% per annum? Also calculate the final amount payable back.
Ans: In this case, the Principal is `1000. The time duration is 5 years and the rate of interest is 8% per annum. So our simple interest will be
The final amount to be paid back will be the original borrowed Principal plus the accumulated interest (Amount = Principal + Simple Interest) and so the final amount payable will be 1000 + 400 =1400.
Now that your concepts are brushed up, let us directly move to some powerful short-cuts that will help you save time
Q2) A certain amount of money doubles itself every four years at a certain simple interest. In how much time will it become six times itself?
Ans: The instant method to solve such questions is to ‘Subtract 1 from the number of times’ that you want. And then multiply itself by the time at which it becomes double. Here we are trying to find out when does the money become 6 times itself.
Therefore, 6 minus 1 gives us 5. Next we multiply 5 with 4 (the time at which it becomes double) So our final answer (5 × 4) is 20. The amount will become six times of itself in 20 years.
Q3) A certain amount of money becomes 3540 in 3 years at 6% interest rate. In how many years will it become 4260 at 7% interest?
Ans: Once again, I will give you a direct formula to solve such types of cases. Remember this rule
So the time is 6 years.
So, you see, using the secret method we quickly get the second part of the answer as 6 years.
Q4) An amount was invested at a simple interest for 2 years. Had it been put at a 4% higher rate, it would have fetched `400 more. Find the amount so invested
Ans: You will often find such twisted questions in competitive exams at the advanced level. Of course you can solve them by the standard formula that you already know. However, my intention in this book is to provide you as many short-cuts as I can so that you can save your time and beat the competition. Remember this direct formula.
Let us now study a direct method of solving compound interest.
COMPOUND INTEREST
In current times, compound interest is a more common form of levying interest. Businesses, finance companies, banks, etc. all use compound interest as the basis for most of their calculations. Many years ago, I was conducting a seminar for bankers and finance professionals. Seated in the audience were 50 odd people eager to learn some mathematical short-cuts from me. All of a sudden, I asked them, “How many of you know how to calculate compound interest?” Almost all of them replied “Yes.” “All right, can you tell me how much will `10,000 become at 11% rate of interest after three years?” I asked. “You may use the calculator on your mobile phones.” All of a sudden there was complete silence in the room. People looked at each other with a confused expression. Barring one or two people, no one knew how to calculate compound interest without their Excel sheets. I offered them two options, either they could use a paper and a pen or a standard calculator.
Most of the participants were hesitant. They said they used Excel or the compound interest calculator app. But given a standard calculator, they had forgotten the method of calculating.
So friends, I am now going to share with you a simple way of calculating compound interest on your calculator. It can even be used while calculating with a pen and paper. This will help you in your daily life when confronted with such situations. Here is how you do it.
Q5) Find the compound interest on `10000 for 3 years at 11%
Ans: Principal is `10000. Time is 3 years. Rate of Interest is 11%
If you go by the standard formula, it will take time. However, have a look at this alternative approach. Here, IR = Interest rate Compound interest = Principal × 1.(IR) (If calculating for 1 year)
Compound interest = Principal × 1.(IR) × 1.(IR) (If calculating for 2 years)
Compound interest = Principal × 1.(IR) × 1.(IR) × 1.(IR)
(If calculating for 3 years)
Compound interest = Principal × 1.(IR) × 1.(IR) × 1.(IR) × 1.(IR)
(If calculating for 4 years) Open the calculator app on your mobile phone
Here the interest rate is 11%, so you will be multiplying with 1.11
And the time duration is 3 years so you will be multiplying the Principal 10000 with 1.11 three times So, punch 10000 × 1.11 × 1.11 × 1.11
This will give you 13676.31 Thus, 10000 will become 13676.31 after 3 years and the compound interest is (13676.31 minus 10000) equals 3676.31
This is the direct method of calculating compound interest on the simple calculator app on your mobile phones. Please share this method with professionals and business people in your circle. In the middle of a meeting, it will really help them.
Q6) If `5000 is compounded at 18% for 2 years, calculate the amount after 2 years.
Ignore writing the formula and writing 5000 [1 + 18/100]2
Instead, you can simply get the answer by multiplying 5000 × 1.18 × 1.18 on your calculator or in your notebook. (1.18 has been taken twice because the duration is 2 years.)
Your final answer will be `6962 I hope you like the direct short-cuts of simple and compound interest that I have shared with you. Whether a student, teacher, professional or a businessperson, you will often be confronted with problems on interest calculation. And in this chapter, we have covered both types of short-cuts (with or without calculator) that you can use. Albert Einstein once said, “Compound Interest is the Eighth Wonder of the World.” He was absolutely correct!
