### Discussion :: Compound Interest - General Questions (Q.No.4)

Ravi said: (Aug 13, 2010) | |

Why do we take 2 r in the half-yearly? |

Anjali said: (Oct 14, 2010) | |

Hello, Since Compound Interest (C.I.) = p[1+{(r/2)/(100)}]^2n for half yearly Thus, C.I.= 5000[1+{(4/2)/(100)}]^{2*(3/2)} =5000[1+{2/100}]^(3) =5306.04 |

Manisha said: (Nov 12, 2010) | |

How we got 3/2 for half yearly for one and half year. please assist. |

Binnu said: (Jan 11, 2011) | |

According to the question no. of years=1 1/2 so it is equal to 3/2 just(2*1+1)/2 |

Sachin said: (Feb 9, 2011) | |

As per formula it should be, C.I. when interest = 5304-5000 = 304 compounded yearly C.I. when interest is = 5306.04-5000 = 306.04 compounded half-yearly Difference = Rs. (306.04 - 304) = Rs. 2.04 |

Manikanta said: (Sep 28, 2011) | |

What about the Compound interest per year? Why do we take [ 1/2 * 4 ] ? |

Mehul said: (Dec 31, 2012) | |

Any shortcut method? |

Deekshit said: (Jul 10, 2013) | |

But the given question is difference b/w year and and half-yearly not as one and half-yearly so the answer is 2.04. |

Srimoyee said: (Jul 17, 2013) | |

The formula is slightly incorrect. Amount = P(1+R/100)^1 + [1+(1/2*R)/100] then C.I = AMOUNT - SUM. Same is in the case of half-yearly. Amount = P(1+R/200)^2*3/2. THEN CI = AMOUNT - SUM. |

Ritesh Kasat said: (Jul 29, 2013) | |

p(1+r/100)^n is value of amount and not compound interest. However if we subtract two amounts, since the principal remains same, we will still get the difference between compound interest only. |

Afsha said: (Dec 13, 2013) | |

Finding it tuff to understand can anyone please make it easy for me from first step. |

Tarun said: (Feb 2, 2014) | |

When interest is compounded annually, Amount = p[1+(r/100)]^t. When interest is compounded half yearly, Amount = p[1+(r/2x100)]^2t. |

Qutub said: (Feb 6, 2014) | |

How "C. I. When interest compounded yearly" is calculated? |

Shakti said: (Mar 19, 2014) | |

When interest is compounded annually~ Yearly, Amount(A) = p[1+(r/100)]^t. CI = P-A.x |

Arslan said: (May 14, 2014) | |

As C.I = [1+4/100]^3/2. = [1+.03]^3/2. = 5302.980298. Why? |

Akshay said: (Jun 24, 2014) | |

Why is is 1+[(1/2)*4/100] when it should be 1+(4/100)^1/2 when the interest is compounded annually. |

Roop said: (Jun 27, 2014) | |

Why 1/2*4 instead of (1+4/100)^1/2 ? |

Roop said: (Jun 27, 2014) | |

@Akshay and @Arslan. When time is in fraction that is 3/2 then the formula is: A = P[(1+R/100)*{1+(R/2)/100). |

Sneh said: (Jun 29, 2014) | |

How we can compound half yearly means I did not understand how 3 can come means n=3 ? |

Divya said: (Jul 8, 2014) | |

Compound interest indicates interest on interest. So we can calculate it as: CI1 = 5000*(4/100)*1 = 200. But I don't know to calculate, CI2 for 1/2 year. Such that compound interest CI = CI1+CI2. |

Simran said: (Aug 24, 2014) | |

How to solve for year and a half when asked in a question please tell me now? |

Shivanath said: (Sep 25, 2014) | |

What is the compound interest formula for full year. Tell the general nth year formula? |

Deepthi said: (Nov 4, 2014) | |

How can we multiply 1/2 along with 4/100 when compounded annually? |

Deepthi said: (Nov 4, 2014) | |

What is the actual equation for CI calculated annually? |

Aswathi said: (Dec 10, 2014) | |

Explanation for the amount when compounded yearly is as below: We learn from our formulas that when interest is compounded, annually but time is in fraction then it should be: Amount = P*(1+r/100)^1*(1+(1/2*4)/100). Please check general formula section 5. |

Gurpreet said: (Feb 6, 2015) | |

For yearly A = P[(1+R/100)*{1+(R/2)/100). Then CI =A-P =304. For half-yearly A = P(1+(R/2)/100)^3. Then CI =A-P =306.04. After that difference = CI(half yearly)-CI(yearly) = [(306.04)-304] = 2.04. |

Stephen Hawking said: (Apr 21, 2015) | |

Correct answer is 3.06. CI 1 = 302.98 (not 304) and CI 2 = 306.04. |

Ranjeeta said: (Jun 3, 2015) | |

When the interest is compounded yearly, for that A = P(1+r/100)^t. = 5000(1+4/100)^1.5 = 5302.98. But here's what they have done I am not getting it for yearly compounding? |

Sowmya` said: (Jun 17, 2015) | |

When time is in fraction formula changes as: For ex time is: 1 1/2 years. = p(1+r/100)^1*(1+(r/2)/100). |

Prach said: (Jun 18, 2015) | |

How 51 come? |

Kajal said: (Jun 18, 2015) | |

Why are you using the formula of amount instead of C.I that means question is demanding for the difference of C.I rather the difference of amount. |

Sangeet said: (Jun 19, 2015) | |

Not understand this question. Why we multiply (1+(((1/2)*4)/100)? Even I am not able understand the further steps. |

Manohar said: (Jun 20, 2015) | |

Hello friends. Thank you for sharing your views about that problem. |

Ayan Guchhait said: (Jul 26, 2015) | |

If the calculator is not provided. Then short cut (same as Given Solution). For yearly (Amount+compound interest) = A (1 + [r/100]) ^ 3/2 A = 5000; are = 4. = A (1 + [r/100]) ^ (1+1/2). = A (1 + [r/100]) * (1 +[r/100] ^ (1/2)). = A (1 + [r/100]) * (1 + 1/2[r/100]). For half yearly (Amount +compound interest) =A (1 +[(r/2) /100]) ^ (3/2*2). |

Keya said: (Sep 14, 2015) | |

If the year was 5 and 1/2 years instead of 3/2 years for annual compound interest then what should be the equation? A = P[(1+R/100)^5*{1+ (R/2) /100). Is it correct? |

Mohit said: (Oct 20, 2015) | |

Any short method without this formula? |

Ritesh said: (Dec 28, 2015) | |

Here formula used for amount but question is for C.I? How? So please check it. |

Chirpy said: (May 18, 2016) | |

How does 26/25 & 51/50 come in the 2nd step? |

Indranil said: (May 18, 2016) | |

If there is any shortcut formula for this? Please assist. |

Akshay said: (May 21, 2016) | |

Direct formula for finding the amount of compound interest. A = P( 1 + R*t/100)^n/t. Where, A : Amount ( principle + interest). P : principle amount. R : rate of interest in %. t : number of years for interested is compounded. n : number of years. In above example, For the half year compounded t=1/2. Try this method. Thanks. |

Varun said: (Jul 15, 2016) | |

Just using a formula of the amount when the interest is compound half yearly, ie time =2n here n = 3/2 then, 2n = 3/2 * 2= 3. |

Lalit Rawat said: (Aug 17, 2016) | |

When interest is compounded half yearly and time is in fraction. A = P(1 + r/2 * 100)^2n. |

Ronak Soni said: (Sep 15, 2016) | |

(1+2/100)^3 in this, why this cube is taken in half yearly? |

Saikumar said: (Sep 28, 2016) | |

Compounded yearly: P = 5000, R = 4% -----> 200, So, 5000 + 200 = 5200, R = 2% -----> 104, Then total = 5200 + 104 = 5304. Compounded half-yearly: P = 5000, R = 2% -----> 100, Then, 5000 + 100 = 5100, R = 2% -----> 102, Then, 5100 + 102 = 5202, R = 2% -----> 104.04, Total = 5202 + 104.04 = 5306.04. And finally, 5304 - 5306.04 = 2.04. |

Deepak said: (Sep 30, 2016) | |

How to decide 4% rate? |

Ashraf said: (Oct 28, 2016) | |

@Saikumar. Why 2% taken? |

Mahalakshmi said: (Dec 21, 2016) | |

What is compound interest formula? First describe it for me. |

Neeraj said: (Dec 24, 2016) | |

Yes @Stephen. I too think the option (b) is the answer. |

Rajjan Khan said: (Dec 25, 2016) | |

Best way. Reffective for yearly = 6.08%, Reffective for half yearly = 6.1208, Difference = .0408%, 5000 *.0408/100 = 2.04. |

Rajjan Khan said: (Dec 25, 2016) | |

Best way. Reffective for yearly = 6.08%, Reffective for half yearly = 6.1208, Difference = .0408%, 5000 *.0408/100 = 2.04. |

Priya said: (Jan 15, 2017) | |

@Rajjan. How you got this? Please explain. |

Krishna said: (Apr 10, 2017) | |

The right ans = 3.06. I agree @Stephen. |

Sangeetha said: (May 10, 2017) | |

Correct answer is 3.06. When the interest is calculated annually, we cannot assume the interest for a half year to be 2%. Hence C.I for 1.5 years should be calculated with n=3/2 and not R=r/2. C.I (annually) - C.I (half-yearly) = 5306.04-5302.98 - 3.06. |

Praveen Kumar C said: (Jun 20, 2017) | |

Actually, the correct answer is 3.06. |

Preethu said: (Jun 27, 2017) | |

What formula are they using for calculating C.I annually? |

Vinay said: (Jun 30, 2017) | |

The exact ans is as follows, Formula for CI = A - P. A - AMOUNT, P - Principle 1/2*4 = 2. = (5000*(1+4/100)^1*(1+2/100)= 5304, Then for only half year 5000*(1+2/100) = 5100, Difference = 5304-5100 = 204 finally u divide by 100 I will get 2.04. |

King said: (Jul 25, 2017) | |

The correct answer is 3.06. |

Maggi said: (Sep 1, 2017) | |

Yes, correct @Saikumar. 4% yearly given in ques. For half year 4/2 =2%. |

Sibatosh Mahata said: (Sep 3, 2017) | |

2.04 is the right answer. |

Indhu said: (Oct 9, 2017) | |

If calculated for half year we should take rate/200 right? Then why rate/100 is taken? |

Krishna said: (Jun 17, 2018) | |

If compound interest is calculated in yearly then compound interest is 302.98 i.e 303. Compound interest=5000[(1+4/100)^1.5-1]. =302.98 i.e 303. So, the calculation of compound interest in yearly is wrong. |

Vinay said: (Aug 10, 2018) | |

The correct answer is 3.06. |

Dheeraj Kumar said: (Aug 18, 2018) | |

When compounded half yearly there is 3 half year will be formed then it must be divided in rate also i.e. 4/3 and then we apply the power as 3. Can anyone please help? |

Rajesh said: (Jan 23, 2019) | |

C.I ON PER YEAR. N=1,1/2 r=4%. P=5000. 1st year-- 5000 in 4% is = 200, Next we need 1/2 year interest so r=4/2. R=2%, Hence 5200 in 2% is = 204. Hence interest is 200+100=304. Then find half year interest. N=3 i.e ::-:'(1*1/2 in 3 half year), R=2 because (4%is full year but we need half yr), 5000 in 2% is =100, 5100 in 2%is =102, 5202 in 2%is =104.04, Total = 306.04. Hence(half year - 1year) = 306.04 - 304. Ans = 2.04. |

Sai said: (Jul 29, 2019) | |

The yearly compound interest in traditional manner 1st 6mnths is 5000* 4/100 = 200. And 2nd 6months is 5200 * 4/100 = 208 the if we add both 200+208=408 how come it's 304? Can anybody explain it? |

S.Naveen said: (Sep 19, 2019) | |

I didn't understand this, please explain me. |

Aashu Patel said: (Dec 1, 2019) | |

Short cut method: Rate given - 4%. CI for yearly, 4%=1/25(first year). 2%=1/50(6 month)(rate divided by 2). 25:26. 50:51. 1250: 1326 //(25*50)and (26*51). 1250x=5000. So x = 4, CI = 1326*4 = 5304. CI for half-yearly, 2% = 1/50(rate divided by 2). 50:51 50:51 50:51 125000:132651 //(50*50*50) and (51*51*51). 125000x = 5000. x = 0.04. So 0.04*132651=5306.04 So difference is 5306.04 - 5304=2.04(answer). |

Paulami Saha said: (Aug 12, 2020) | |

When interest is compounded yearly then we calculate the time = 1 1/2. When interest is compounded half-yearly, then we calculate the time = (1 1/2)/2 = 3/2*2=3. |

Mamta Dahal said: (Mar 31, 2021) | |

By the question; CI yearly - CI half yearly. P((1+R÷100)^n-1)- p((1+R÷200)^n)-1). = 5000((1+4÷100)^3÷2-1)-5000((1+4÷200)^3-1). = 306.04-302.98. = 3.06. |

Gunjan Patidar said: (Apr 5, 2021) | |

I too agree the answer is 3.06. |

Nikhil said: (Jun 16, 2021) | |

We can do the same thing for both C.I. We don't need to do extra stuff like 3/2 and all just try I got my answer correctly without using this method. |

Amar said: (Oct 24, 2021) | |

I think the right Answer is 3.06. |

Mhaske Omkar said: (Jan 5, 2022) | |

1*1/2 means 3/2 means 18 months. Calculate C.I. for half-yearly 3 times add them which will be 306.04. Calculate C.I. for yearly then add the first half-yearly C.I. which will be 200+104 = 304. Calculate the difference of both is 2.04. |

Mona said: (May 7, 2022) | |

Can someone please explain the calculation of C.I for yearly basis? I am not getting this. |

Mayur said: (Jul 11, 2022) | |

As we know that, The formula for annual compound interest, including principal sum, is: A = P (1 + r/n) (nt). Where: A = the future value of the investment/loan, including interest P = the principal investment amount (the initial deposit or loan amount) r = the annual interest rate (decimal) n = the number of times that interest is compounded per year t = the number of years the money is invested or borrowed for C.I. when interest compounded yearly = Rs. 5000 * (1 + 4/100) * (1 + (4/2) /100) = Rs.(5000 * 26/25 * 51/50) = Rs. 5304. C.I. when interest is compounded half-yearly = Rs. 5000 * (1 + 2/100) 3 = Rs.(5000 * 51/50 * 51/50 * 51/50) = Rs. 5306.04, Difference = Rs.(5306.04 - 5304) = Rs. 2.04. |

K. Anzi said: (Aug 7, 2022) | |

Can we take time (n) in fraction as 3/2 in the yearly formula? Please explain me. |

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