The Compound Interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. In simple words, we can say that when you get interested on your invested money and interest in that money. Show
Simple interest means when you get interested in your principal amount only. But the compound interest is the interest on the principal sum and the interest earned on it. The formula of compound interest is: A = {1 + R/100} ᵀ Here T = Time A = Amount P = Principal R = Rate of Interest A = Amount = Principal + Compound Interest In this article, you will get to know all the tips to solve Compound Interest Questions for NID How to Solve Compound Interest Questions for NID 2023?Compound Interest is an extension of Simple Interest. If you have understood the topic of simple interest thoroughly then you can easily understand the topic of compound interest as well and score good marks in the NID entrance exam. When it comes to understanding compound interest we need to understand that simple interest has an anomaly. The anomaly was that whatever interest was generated was not getting added to the principal because whatever interest is getting generated year after year that interest still stays with the person who has borrowed the money. Download Free Practice Question Papers for NID Exam by CreativeEdge And he is not returning you the money each after each, he will return you the money when the entire amount is accumulated and after the entire duration finally when he returns you the amount in that amount the principal and interest amount is returned to you. This happens in simple interest. And, what compound interest tells us is that it keeps on adding the interest generated in the principal amount. So, what happens in compound interest is the principal keeps on getting updated every year. The compound interest is not just a concept to be used to solve the questions related to compound interest but also the questions related to appreciation, depreciation of assets, decrease or increase of population, and etc. Some of the major question types which are asked in the simple interest and compound interest are as follows: -
How to prepare simple and compound interest for NID 2023?The following are some of the tips that will help enhance your NID exam preparation.
There are some of the questions mentioned below with their solution that will help you to get the tips to solve compound interest questions for NID. Read more: Previous year exam analysis for NID entrance exam Question 1: A bank charges a rate of interest of 10% compounded annually. What is the total amount to be paid on a loan of Rs. 36000 for 3 years? Answer: The total amount to be paid = 47916. Explanation: In this question, we will consider the simple interest and compound interest both because that will help you to understand the difference between them easily. Given: Rate of Interest = 10% compounded annually Principal Amount = Rs. 36000 Time = 3 years To find: interest amount to be paid in 3 years Solution : Principal amount = 36000 Simple interest for 3 years Interest Amount = Principal x rate of interest x time Interest Amount = 36000 x 10% x 3 years Interest Amount = 36000 x 10/100 x 3 Interest Amount = 10800 Therefore, the simple interest amount for 3 years will be Rs. 10800 and for each year it will be Rs. 3600. Compound interest for 3 years Amount = {1 + Rate/100} ᵀ Read more: Important questions with answers for the NID CAT exam We will use the box method to solve this question. We will calculate interest for 3 years. We will calculate 10% of 36000 i.e. Rs. 3600 Then we will write in the boxes mentioned below Rs. 3600 will be the interest that you will get every year that’s why we have written 3600 in each year box. Now, we will calculate 10% of 3600 for 2nd-year compound interest i.e. 360 So, the 2nd year interest is 3600 + 360 = 3960 as you can see in the box below. Then for the 3rd year, we will calculate 10% interest on 3600 of 1st year and 3600 of 2nd year i.e. 10% of 7200 i.e. 720. And 10% interest of 360 i.e. 36 So, the 3rd year interest is 3600 + 720 + 36 = 4356 as you can see in the box below. So, Compound interest (CI) = 3600 (1st year) + 3960 (2nd year) + 4356 (3rd year) = 11916 Compound interest (CI) = 11916 Amount = Principal + Compound Interest Amount = 36000 + 11916 Amount = 47916 Question 2: If P = 10000/-, T = 2 years 6 months, rate of interest = 20% compounded annually. Find Amount. Answer: Amount = Rs. 15840 Explanation: We will use the box method to solve this question. We will calculate interest for 3 years. We will calculate 20% of 10000 i.e. Rs. 2000 Then we will write in the boxes mentioned below Rs. 2000 will be the interest that you will get every year that’s why we have written 2000 in each year box. Now, we will calculate 20% of 2000 for 2nd-year compound interest i.e. 400 So, the 2nd year interest is 2000 + 400 = 2400 as you can see in the box below. Then for the 3rd year, we will calculate 20% interest on 2000 of 1st year and 2000 of 2nd year i.e. 20% of 4000 i.e. 800. And 20% interest of 400 i.e. 80. But in the question, they have asked only the interest of 2 years and 6 months. So, we will take interest of 2 years full and half interest of 3rd year Read more: Best study timetable to enhance your NID preparation So, Compound interest (CI) = 2000 (1st year) + 2400 (2nd year) + 1440 (6 months) = 5840. Compound interest (CI) = 5840. Amount = Principal + Compound Interest Amount = 10000 + 5840 Amount = 15840 Question 3: If P = 20,000, Rate of Interest = 3% p.a. Time = 2 years 3 months, Find Compound interest. Answer: Compound Interest (CI) = Rs. 1377.135. Explanation: We will use the box method to solve this question. We will calculate interest for 3 years. We will calculate 3% of 20000 i.e. Rs. 600 Then we will write in the boxes mentioned below Rs. 600 will be the interest that you will get every year that’s why we have written 600 in each year box. Now, we will calculate 3% of 600 for 2nd-year compound interest i.e. 18 So, the 2nd year interest is 600 + 18 = 618 as you can see in the box below. Then for the 3rd year, we will calculate 3% interest on 600 of 1st year and 600 of 2nd year i.e. 3% of 1200 i.e. 36. And 3% interest of 18 i.e. 0.54. But in the question, they have asked only the interest of 2 years and 3 months. So, we will take interest of 2 years full and 1/4th interest of 3rd year So, Compound interest (CI) = 600 (1st year) + 618 (2nd year) + 159.135 (3 months) = 1377.135 Compound Interest (CI) = 1377.135 Read more: Important questions for the NID CAT exam Question 4: If P = 7.30 lacs, Rate of Interest = 10% p.a. T = 2 years and 2 days. Find Compound Interest. Answer: Compound Interest (CI) = Rs. 1,53,784. Explanation: We will use the box method to solve this question. We will calculate interest for 3 years. We will calculate 10% of 7,30,000 i.e. Rs. 73000 Then we will write in the boxes mentioned below Rs. 73000 will be the interest that you will get every year that’s why we have written 73000 in each year box. Now, we will calculate 10% of 73000 for 2nd-year compound interest i.e. 7300 So, the 2nd year interest is 73000 + 7300 = 80300 as you can see in the box below. Then for the 3rd year, we will calculate 10% interest on 73000 of 1st year and 73000 of 2nd year i.e. 10% of 1,46,000 i.e. 14600. And 10% interest of 7300 i.e. 730. But in the question, they have asked only the interest of 2 years and 2 days. So, we will take interest of 2 years full and 2 days interest of 3rd year So, Compound interest (CI) = 73000 (1st year) + 80300 (2nd year) + 484 (2 days) = 1,53,784 Compound Interest (CI) = 1,53,784 Question 5: If P = 18000, Rate of Interest = 16.66%, Time = 1 year 73 days, Find Compound Interest. Answer: Compound Interest (CI) = Rs. 3700 Explanation: We will use the box method to solve this question. We will calculate interest for 2 years. We will calculate 16.66% (1/6) of 18000 i.e. Rs. 3000 Then we will write in the boxes mentioned below Rs. 3000 will be the interest that you will get every year that’s why we have written 3000 in each year box. Now, we will calculate 16.66% (1/6) of 3000 for 2nd-year compound interest i.e. 500 So, the 2nd year interest is 3000 + 500 = 3500 as you can see in the box below. But in the question, they have asked only the interest of 1 year and 73 days. So, we will take interest of 1 year full and 73 days interest of 2nd year So, Compound interest (CI) = 3000 (1st year) + 700 (73 days) = 3700 Compound Interest (CI) = 3700 Question 6: If P = 10400, Rate of Interest = 5%, Time = 1 year and 6 weeks, interest compounded annually. Answer: Compound Interest (CI) = Rs. 583 Explanation: We will use the box method to solve this question. We will calculate interest for 2 years. We will calculate 5% of 10400 i.e. Rs. 520 Then we will write in the boxes mentioned below Rs. 520 will be the interest that you will get every year that’s why we have written 520 in each year box. Now, we will calculate 5% of 520 for 2nd-year compound interest i.e. 26 So, the 2nd year interest is 520 + 26 = 546 as you can see in the box below. But in the question, they have asked only the interest of 1 year and 6 weeks. So, we will take interest of 1 year full and 6 weeks interest of 2nd year So, Compound interest (CI) = 520 (1st year) + 63 (6 weeks) = 583 Compound Interest (CI) = 583 Read more: Important questions for the NID GAT exam Question 7: If P = 8000, Time = 3 years, Rate of Interest = 1%, 2%, and 3%. Find CI – SI =? Answer: Compound Interest – Simple Interest = Rs. 7.248 Explanation: We will use the box method to solve this question. We will calculate interest for 3 years. Given that every year rate of interest changes i.e. 1st-year rate of interest is 1% 2nd-year rate of interest is 2% 3rd-year rate of interest is 3% To find: Compound Interest – Simple Interest Let x be the simple interest of all year Let y be the compound interest of 2nd and 3rd year Let z be the compound interest of 3rd year Now see below Compound interest = x + x + y + x + 2y + z Compound interest = 3x + 2y + z Simple Interest = x + x + x Simple Interest = 3x Compound Interest – Simple Interest = 3x + 2y + z – 3x Compound Interest – Simple Interest = 2y + z ----- equation 1 Equation 1 shows the difference between Compound Interest and Simple Interest is always written on the box. Please analyze equation 1 and the 3rd year box so you will understand everything. We will calculate 1% of 8000 i.e. Rs. 80 Then we will write in the boxes mentioned below Rs. 80 will be the interest of 1st year We will calculate 2% of 8000 i.e. Rs. 160 Rs. 160 will be the interest of 2nd year We will calculate 3% of 8000 i.e. Rs. 2400 Rs. 240 will be the interest of 3rd year Now, we will calculate 2% of 80 for 2nd-year compound interest i.e. 1.6 So, the 2nd year interest is 160 + 1.6 = 161.6 as you can see in the box below. Then for the 3rd year, we will calculate 3% interest on 80 of 1st year and 160 of 2nd year i.e. 3% of 240 i.e. 7.2 And 3% interest of 1.6 i.e. 0.048. So, we will take interest in 3rd year And as you have analyzed above that Compound Interest – Simple Interest = 2y + z So, Compound Interest – Simple Interest = 7.2 + 0.048 Compound Interest – Simple Interest = 7.248 Question 8: The differences between Simple interest and compound interest on a certain sum of money at 5% for 2 years are Rs. 3. Find the sum? Answer: Sum = Rs. 1200 Explanation: In this question, there is no principal amount given so we can’t apply the box method here. So, here we have to approach differently i.e. we will see the rate of interest. In the question, it is given the rate of interest is 5% and time is 2 years Convert 5% interest into fraction i.e. 1/20 Now, look at the time It is 2 years given So, we will square the fraction part of the interest and the base value of that fraction will be our assumed principal amount. Let Principal = (20) ² Principal = 400 Now we have the principal amount now we can apply the box method We will use the box method to solve this question. We will calculate interest for 2 years. We will calculate 5% of 400 i.e. Rs. 20 Then we will write in the boxes mentioned below Rs. 20 will be the interest that you will get every year that’s why we have written 20 in each year box. Now, we will calculate 5% of 20 for 2nd-year compound interest i.e. 1 So, the 2nd year interest is 20 + 1 = 21 as you can see in the box below. As you know, the difference between Compound Interest and Simple Interest of 2 years is Y. So, Here Y = 1 And 1 = Rs. 3 (given in question) We have to find the actual principal So, if 1 unit = Rs. 3 Then, 400 units = Rs. 3 * 400 i.e. Actual Principal or Sum = Rs. 1200 Question 9: If the difference between Compound interest and simple interest on a certain sum of money at 5% p.a. for 3 years is Rs. 122. Find the sum. Answer: Sum = Rs. 16,000 Explanation: In this question, there is no principal amount given so we can’t apply the box method here. So, here we have to approach differently i.e. we will see the rate of interest. In the question, it is given the rate of interest is 5% and time is 3 years Convert 5% interest into fraction i.e. 1/20 Now, look at the time It is 3 years given So, we will cube the fraction part of the interest and the base value of that fraction will be our assumed principal amount. Let Principal = (20) ³ Principal = 8000 Now we have the principal amount now we can apply the box method We will use the box method to solve this question. We will calculate interest for 3 years. We will calculate 5% of 8000 i.e. Rs. 400 Then we will write in the boxes mentioned below Rs. 400 will be the interest that you will get every year that’s why we have written 400 in each year box. Now, we will calculate 5% of 400 for 2nd-year compound interest i.e. 20 So, the 2nd year interest is 400 + 20 = 420 as you can see in the box below. Then for the 3rd year, we will calculate 5% interest on 400 of 1st year and 400 of 2nd year i.e. 5% of 800 i.e. 40 And 5% interest of 20 i.e. 1 As you know, the difference between Compound Interest and Simple Interest of 3 years is 2Y + Z. So, Here 2Y + Z = 61 And 61 = Rs. 122 (given in question) We have to find the actual principal So, if 1 unit = Rs. 2 Then, 8000 units = Rs. 2 * 8000 i.e. Actual Principal or Sum = Rs. 16000 Question 10: Simple interest on a sum of money for 2 years is Rs. 480 and Compound interest is Rs. 492. Find the sum and rate of interest. Answer: Principal amount = Rs. 4800 Rate of interest = 5% Explanation: Given: Time = 2 years Simple interest = Rs. 480 Compound Interest = Rs. 492 To Find Sum and Rate of Interest. We have simple interest i.e. Rs. 480 So, this simple interest is of 2 years. It means that for each year you are getting Rs. 240 as simple interest. And we have compound interest also i.e. Rs. 492. Now see the box method So as you see if you have both SI and CI then We can find the rate of interest like this: =) 240 * R/100 = 12 =) R = 5% Rate of interest = 5% When we find principal amount the formula is =) P * R/100 = SI of 1 year =) P * 5/100 = 240 =) P * 1/20 = 240 =) P = 240 * 20 =) P = 4800 So, Principal amount = Rs. 4800 And, rate of interest = 5% Question 11: Principal =? Time = 3 years, Rate of Interest = 15%, Compound interest – Simple interest = Rs. 1701. Answer: Sum = Rs. 24000 Explanation: In this question, there is no principal amount given so we can’t apply the box method here. So, here we have to approach differently i.e. we will see the rate of interest. In the question, it is given the rate of interest is 15% and time is 3 years Convert 15% interest into fraction i.e. 3/20 Now, look at the time It is 3 years given So, we will cube the fraction part of the interest and the base value of that fraction will be our assumed principal amount. Let Principal = (20) ³ Principal = 8000 Now we have the principal amount now we can apply the box method We will use the box method to solve this question. We will calculate interest for 3 years. We will calculate 15% of 8000 i.e. Rs. 1200 Then we will write in the boxes mentioned below Rs. 1200 will be the interest that you will get every year that’s why we have written 1200 in each year box. Now, we will calculate 15% of 1200 for 2nd-year compound interest i.e. 180 So, the 2nd year interest is 1200 + 180 = 1380 as you can see in the box below. Then for the 3rd year, we will calculate 15% interest on 1200 of 1st year and 1200 of 2nd year i.e. 15% of 2400 i.e. 360 And 15% interest of 180 i.e. 27 As you know, the difference between Compound Interest and Simple Interest of 3 years is 2Y + Z. So, Here 2Y + Z = 1701 And 567 = Rs. 1701 (given in question) We have to find the actual principal So, if 1 unit = Rs. 3 Then, 8000 units = Rs. 3 * 8000 i.e. Actual Principal or Sum = Rs. 24000 Question 12: A man borrowed Rs.80000 at the rate of 10% p.a. compound interest, interest being compounded annually. How much amount should he have repaid at the end of the first year, if by repaying Rs.55000 at the end of the second year he can clear the loan?
Answer: 1. Rs. 38000 Explanation: Principal= 80000 Rate of interest = 10 % ‘ after first year amount = 88000 10 % rate compounded annually If we paid 55000 at the end of the 2nd year it means we paid 110 % of the amount left after paying certain from the 1st year. CI always calculated on the previous year amount. =55000/110 * 100 = 50000 So that certain amount is paid after the first year then the remaining amount is equal to 50000. i.e the certain amount paid after 1st year is equal to the = 88000-50000 = 38000 Question 13: A certain loan amount, under compound interest, compounded annually earns an interest of Rs.1980 in the second year and Rs.2178 in the third year. How much interest did it earn in the first year?
Answer: 2. Rs. 1800 Explanation: Interest in 2nd year = 1980 Rs. Interest in 3rd year = 2178 Rs. Difference=2178-1980=198 Rae of interest = (198/1980)*100 = 10% If the rate of interest is 10 % compounded annually then the interest in the second year is 11 % It means 1980 is 11% and we have to calculate first year i.e we have to calculate 10 % of p The interest of 1st year = 1980/11*10 = 180*10 = Rs. 1800/- Question 14: A sum of money under compound interest doubles itself in 4 years. In how many years will it become 16 times itself?
Answer: 2. 16 years Explanation: if time is constant then the ratio of principal and amount is always constant in compound interest. in 4 years sum become doubled P become 2P p _____4 years ____2p___4years _____8p ___4 years ____ 16 4+4+4+4= 16 years Question 15: A sum of money is lent at a certain rate of interest at compound interest. If, instead the same amount was lent at simple interest the interest for the first two years reduces by Rs.160 and that for the first three years reduces by Rs.488. Find the sum
Answer: 4. Rs. 64000 Explanation: B is the difference B/w 2 years of interest So B = 160 Difference B/w 3 years of C. I and S.I = 3B+C = 488 160*3+C = 8 C is calculated on 8 Rate = 8/160*100 = 5% A = 160/5*100 = 3200 P = 3200/5*100 P = Rs. 64,000 What sum will the compound interest at 5% per annum for 2 years compounded annually be rupees 164?100×4×16441=Rs. 1600.
On what sum will the compound interest at 5% per annum for 2 years compounded annually?Thus, the required sum is Rs. 1600.
On what sum will the compound interest at 5% per annum for 2 years compounded annually be Rs 3280 a RS 32000 B Rs 16000 C RS 48000 D RS 64000?Thus, required sum is Rs. 1600.
On what sum will the compound interest at 5 for 2 years?On what sum will the compound interest at 5% p.a. for 2 years compounded annually be Rs. 3,280.
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