### Discussion :: Compound Interest - General Questions (Q.No.3)

Subash said: (Jul 22, 2010) | |

Please explain the use of -1 in C.I calculation. I think here we have to subtract the principle at the back. But u use the value '1' here, I can't understand Wat u r did. But i got the same answer by using the formula. C.I = (Amount - Principle) Where Amount = {P x (1 + (R/100)^N)} - P P = 12000. Therefore, C.I = Rs. (12000*(1+(10/100)^3))-12000 = 3972 |

Javeed said: (Jul 28, 2010) | |

Dude here principle is Rs. 12000, so amount = P(1+r/100)^t C.I = amount - principle i.e., p((1+r/100)^t )-p Removing 'p' common factor we get: p((1+(R/100)^T)-1) HERE 1200 IS REMOVED AS COMMON FACTOR SINCE IT IS THE VALUE OF P. |

Priya said: (Jul 31, 2010) | |

Thanks Jeeva. Now I also clear abut this problem. |

Anurag said: (Oct 18, 2010) | |

Thanks a lot. Now it became very easy. |

Kusum said: (Feb 12, 2011) | |

Any one tel me how we got R value as 10? |

Amit said: (Apr 18, 2011) | |

@Kusum Simple interest formula SI = PRN / 100 So, SI * 100 = PRN which derives new formula for R as R = (SI * 100) / PN Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years. Put all this into simple interest formula R = (100 x 60 ) / 100 x 6 = 10% p.a. Hope you will get it :) |

Karthi said: (Aug 3, 2011) | |

How we get P = Rs.100 and S.I = Rs. 60 ? |

Arush said: (Sep 15, 2011) | |

Thanks jeeva & subash. |

Vasanth said: (Oct 5, 2011) | |

Why we should take p value as 100? |

Anmol said: (Oct 21, 2011) | |

@Karthi & Vasanth: you can take any value of P instead of 100. 100 is taken just for simplicity of calculation. Now, as there is 60% rise in principal in 6 years therefore, Net amount after 6 years, A= P+ 60% of P =1.6P therefore interest,I= 1.6P-P= .6P using SI formula, I= PTR/100 so, 0.6P= P*6*R/100 -> 60=6R -> R=10% |

Shalini said: (Nov 28, 2011) | |

I'm totally confused with these problems. When compound interest is done by individual formulas the answer shows wrong. |

Poorvajain said: (Jan 2, 2012) | |

CI=AMT-PRINCIPLE So in this question princple is 100 and u hve taken principle 1 why so is it wrong. |

Yamini said: (Mar 4, 2012) | |

@Subash There was no confusion in the given answer, here -1 is nothing but as you said Amount = {P x (1 + (R/100)^N)} - P so from this just take common as P then you get Amount=[P x {(1 + (R/100)^N)-1}]. |

Dibyajyoti Hazarika said: (Mar 6, 2012) | |

I'm confused about 331 no. How it comes? |

Neha said: (Apr 11, 2012) | |

@dibyajyoti Hazarika. (1+ 10/100)^3 -1 After L.C.M. it will be {(100+10)/100}^3 -1 (110/100)^3 -1 (11/10)^3 -1 //(11x11x11=1331)and (10x10x10=1000) (1331/1000)-1 After L.C.M. (1331-1000)/1000 331/1000 I think now you understand about 331 |

Sunita Sisodiya said: (May 23, 2012) | |

Can you help with shortcut method for the same. |

Sandip said: (Mar 24, 2013) | |

C.I = Rs. (12000*(1+(10/100)^3))-12000 = 3972. |

Deepthi said: (May 2, 2013) | |

How we get S.I=Rs.60 while P=Rs.100 ? |

Vicky said: (May 9, 2013) | |

Formula for C.I, Amount = p(1+R/100)^N, Where amount = Principal + C.I. Principal + C.I = p(1+R/100)^N. C.I = p(1+R/100)^N - Principal, ' p ' is a common factor. C.I = p [(1+R/100)^N-1]. |

Rajata said: (Oct 9, 2013) | |

Its totally wrong hear as compound interest 1200(1+r/1000)n. As the given formula it should be 12000*1331/1000. So the answer is..15972. |

Steve said: (Dec 4, 2013) | |

You make your calculation too complicated for beginners, it would have been much more easier if you just convert it to decimal and ignore the fraction thing. Good job though. |

Aayushi said: (Jan 21, 2014) | |

Can anyone help me that why do we have to subtract the P. And when to subtract and when not to? |

Sarojkumarnaik786@Gmail.Com said: (Apr 26, 2014) | |

Generally we know the formula of amount not C.I. Amount = P(1+ R\100)^t. If we find C.I then we should subtract the principal, then the formula changes to C.I = P((1 + R/100)^t -- 1). |

Bhoomika said: (May 25, 2014) | |

What is -1 ? |

Nivedita said: (Jun 17, 2014) | |

How you have taken P as 100 ? |

Satya said: (Jul 24, 2014) | |

60% is equal to 60/100 i.e., S.I means adding same rate of interest every year, So here we knew that 60% is increased in 6 years, i.e., Every year it is increased by 10%. So that 10% * 6 years= 60% for 6 years. So that rate of interest = 10%. |

Satya said: (Jul 24, 2014) | |

@Nivedita. Don't bother about 'P'. Think logically about r% using given data. |

Josephlecocq said: (Oct 29, 2014) | |

Is -1 the same as p? |

Angita said: (Nov 8, 2014) | |

How SI was 60? |

Sandeep said: (Dec 28, 2014) | |

Please explain How (1+10/100)^3 is calculated? |

Aparna said: (Jul 3, 2015) | |

How could it come 331/1000? Shall anyone explain me please? |

Hari said: (Jul 12, 2015) | |

How to find p=100? |

Rohani said: (Jul 27, 2015) | |

Why we take S.I as 60 and what is the difference between S.I and C.I? |

Aditya said: (Sep 9, 2015) | |

S.I is interest on Principle. C.I is interest of interest. |

Beaulah Abigail said: (Sep 27, 2015) | |

How the formula C.I = Amount-P comes? |

Rahul said: (Oct 21, 2015) | |

Brother the answer should be 3852 and a simpler method could be 10 percent of 12000 = 1200 + 10% of 12000 + 10% of 1200 = 1200 + 120 and so on the last will be 1200 + 120 + 12 so grand total 3852. |

Prasad said: (Oct 26, 2015) | |

Sir question says there is an increase of 60% in amount. How can you take 60 as SI? |

Pavan said: (Nov 2, 2015) | |

I am getting confusion on this problem can anyone tell me in easy way. |

Lee Chong Wei said: (Nov 28, 2015) | |

Hi can anyone explain me why CI = Amount-P if its P we can substitute the actual principal. |

Dearlie Beloved said: (Dec 30, 2015) | |

'I' means increase, since I=F-P. Taking 60 as SI while letting P=100 in i=I/Pn assumes that the future amount will be 60 greater than 100. We can let P as any number, say P=210, but we need to change I=150 to signal 60 in increase of future amount. We only put P=100 to give justice to the percent sign after 60. And compound interest is what was asked and not CI rate? Hope this helped. |

Vani said: (Jan 23, 2016) | |

Suppose principle is 100. Then simple interest becomes 60. Then rate will become 10% by using the formula, (ptr)/100 = simple interest. Now the compound interest in 3 years with the rate 10% is, 10+10+1(interest on interest)+11+1.1 = 33.1. 12000 --- 100 ?----------- 33.1 The answer is 3972. |

Durga said: (Jun 6, 2016) | |

@ All, Guys your discussions are very useful. Thank you all. |

Thejus said: (Jul 29, 2016) | |

@Josephlecocq. What is -1 as p? |

Vikash said: (Jul 31, 2016) | |

After taking common factor p from bracket then automatically -1 come i.e. -1 * p = -p. If you are confused about -1 then don't take common answer come same but it becomes some complicated. |

Prabhakaran said: (Aug 3, 2016) | |

Hi, can anyone explain to me why CI = Amount - P if its P we can substitute the actual principal. |

Malleswar said: (Aug 5, 2016) | |

Beautifully explained. Thanks to all. |

Arvindsamy said: (Aug 11, 2016) | |

Guys your discussions and solutions are very useful. Thank you all guys. |

Blessing said: (Aug 16, 2016) | |

The formula for compound interest:. A = P (1 + r) ^n. Now, P = 12000. A = ? N = 3. From the first statement, there was 60% increase in an amount for 6 years simple interest. Let the amount (P) be 100 then SI=60, SI = PIN. 60 = 100 * I * 6, 60 = 600 I, I = 0.1. Since we have 0.1 x 100 = 10%. Now A = 12000 (1 + 1/10)^3 = 12000 (11/10)^3, = 12000 (11/10 x 11/10 x 11/10), = 12000 (1331/1000) = 15,972. So, A = 15972, P = 12000 then, CI = 15972 - 12000 = 3972. |

Renu said: (Nov 13, 2016) | |

10% successive of 3 years is 33.1% 33.1% of 12000. = 3972. |

Angad said: (Jan 5, 2017) | |

How to find the rate of interest if compound interest and principle and time is already given but the rate is missing? I need the solution. |

Malinimadhavan said: (Feb 5, 2017) | |

@Angad. Formula to find the rate of interest from ci is r= n[(A/P)^1/nt -1]. Now take p=12000; amount (A) = C.I + PRINCIPLE (3972+12000) = 15972; time(t) = 3years n=1. By substituting this values in the above equation. r = 1[(15972/12000)^1/3 -1], = [(1.331)^1/3 -1], r = [1.1-1], r = 0.1. To calculate rate of interest in percentage we use R = r*100. Therefore R = 0.1*100 = 10%. Thus rate of interest is 10% p.a. I hope it will help you. |

Victor said: (Feb 7, 2017) | |

Please help me to solve this question. Formula: Fp=Pp(1+r) raise to power n. if Pp=100, r=3%,n = 10. |

Sammy said: (Feb 23, 2017) | |

Thank you so much for explaining the solution. |

Sanjay said: (Apr 14, 2017) | |

60% is equal to 60/100 i.e., S.I means adding the same rate of interest every year, So here we knew that 60% is increased in 6 years, i.e., Every year it is increased by 10%. Then, caculate net % for 3yrs. i.e. Calculte 1st (10%)and 2nd yr(10%).then result with 3rd yr(10%). i.e 10+10+(10 * 10)/100 = 21. Next 21+10+(21 * 10)/100 = 33.1%. So now just calculate 33.1%12000. i.e 3972. |

Sudarsan said: (Jun 17, 2017) | |

Thanks @Neha. |

Manisha said: (Jun 25, 2017) | |

Thanks @Sanjay. |

Dron said: (Jul 27, 2017) | |

How to find p=100? |

Saleem said: (Oct 19, 2017) | |

60%increase in 6 yrs. i. e 10%every yr. i. e R=10%. Now A=P(1+10/100)^3=1200(1+1/10)^3=15972. CI=15972-12000=3972. |

Riya said: (Oct 31, 2017) | |

helpful |

Mohammad Gazali said: (Nov 19, 2017) | |

Please tell me how R=100*60/100*6? |

Lokesh said: (Nov 20, 2017) | |

How Will find P & S.I? |

Moni Shankar said: (Dec 10, 2017) | |

1200*(11/10)*(11/10)*(11/10)=15972. CI=15972-12000=3972, P.S : (HERE 11/10=110/100 WHICH MEANS 10% RATE AND CAME FROM STATEMENT 60% INCREMENT IN 6 YEARS.) |

Aashi said: (Jul 9, 2018) | |

Please tell me how 331 is coming? Please explain me. |

Rajeev Rathor said: (Aug 26, 2018) | |

Using pascal traingle. = 3*10%of12000+3*10%of1200+1*10%of120, = 3600+360+12, = 3972. |

Shub said: (Oct 20, 2018) | |

Amount after 1st year =1200. After 2nd year=1200 + 120. After 3rd year= 1200 + 120+120+12. Total = 3972. |

Bhushan said: (Dec 1, 2018) | |

SI for 6 yrs increase by 60%. Means; For 1st yr 10%. 1st yr , 10% of 12000 = 1200 - - - >(1) Add 1200 ... ie. = 12000+1200= 13200. For 2nd yr, 10% of 13200 = 1320 - - - > (2) So, 13200+1320= 14520. For 3rd yr, 10% of 14520 = 1452. - - - > (3) So add the interest amount of all 3 equations ie.... 1200 + 1320 + 1452 = 3972 is the right answer. |

Ganesh said: (Dec 5, 2018) | |

@All. 1st find rate R of 6 yr Assume 100rs, for 6 yr. R=(100 * s.i/p * n) = 10%. After that find C.I using ratio proposition of 3 yr is 3:3:1 is fixed and 2yr is (2:1). Then 1st yr c.i. is 3* 10% of 12000, 2nd yr C.I is 3* 10% of 1200, 3rd yr C.I is 1* 10% of 120 add all the yrs. 3600 + 360 + 12 = 3972 is the answer. |

Sangavi said: (Dec 9, 2018) | |

When will we use -P in the compound interest formula? |

Rahul Krishna said: (Oct 3, 2019) | |

Let p=100 and si=60(as amount increase to 60%). Si=(p*r*t)/100. Find r=?. Then, with the help of r find ci. |

Rahul Krishna said: (Oct 3, 2019) | |

@Sangavi we use - p because. CI = Amount - principal. So, CI=p(1+r/100)^n-p. |

Hari said: (Nov 17, 2019) | |

Why we are calculating for 3 years? |

Shri said: (May 18, 2020) | |

Thanks for explaining @Anmol. |

Ronald said: (Jul 3, 2020) | |

12000 in 10% is 1200 then, 12000+1200=13200 is 1st year. And 13200 in 10% so 13200+3200= 16400. Same next year we get 16400+6400=18040. Then, 18040-12000=6040. Why not like this? Anyone explain to me. |

Sai said: (Jul 3, 2020) | |

12000 in 10% is 1200. So 1st year 12000+1200 = 13200. 13200 in 10 % is 1320 so 13200 + 1320 = 14520. Next 3rd year 14520 in 10% is 1452 so, 14520 + 1452 = 15972. So, finally 15972 - 12000 = 3972. |

Ramya C said: (Jul 12, 2020) | |

Anyone can explain me, why we are calculating for 3 years? |

Taraka said: (Aug 15, 2020) | |

A = p+si P(160/100) = p + (p*6*R). R = 10%. Next; A = p+ci. A = 12000 * (110/100) ^3 P = 12000. Then substituting a and p then; Ci = 3972. |

Katherin said: (Sep 18, 2020) | |

I'm confused on using -1. Why it is used? Please anyone explain. |

Pratiksha said: (Dec 30, 2020) | |

@Katherin, Instead of -1 you can take principal amount( in this case -12000/-), you will get the same answer. |

Banshika said: (Jan 21, 2021) | |

If the amount is increased by 60%. It should be 160 right? Then why they took 60 straight to find the answer? |

Sriram Manikanth said: (Jan 22, 2021) | |

60 is interest 100 is the principle. SI = pnr/100. Therefor 60 = 100 * 6*r/100, r = 10%. |

Keerthi said: (May 29, 2021) | |

1200*{(1+10/100)^3 - 1}, and next step how will become? Especially- (1200*331/1000). Please explain to me. |

Harshit said: (Sep 30, 2021) | |

How to solve (1 + 10/100) ^3? Please explain it. |

Vishwanath said: (Apr 4, 2022) | |

@Harshit. First solve brackets, then multiply them into 3 times. Then, You will get 1331/1000. |

Vishwanath said: (Apr 4, 2022) | |

@Keerti. 12000 * 331/1000 = 12 * 331/1 = 3972. |

Kal El said: (Jul 3, 2022) | |

There is a difference between 'increase to' and 'increase by'. So, please describe it clearly to understand. |

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