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# Aptitude - Compound Interest - Discussion

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"You cannot shake hands with a clenched fist."
- Indira Gandhi
1.

A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

 [A]. Rs. 120 [B]. Rs. 121 [C]. Rs. 122 [D]. Rs. 123

Explanation:

Amount
 = Rs. 1600 x 1 + 5 2 + 1600 x 1 + 5 2 x 100 2 x 100
 = Rs. 1600 x 41 x 41 + 1600 x 41 40 40 40
 = Rs. 1600 x 41 41 + 1 40 40
 = Rs. 1600 x 41 x 81 40 x 40
= Rs. 3321.

C.I. = Rs. (3321 - 3200) = Rs. 121

 Akhila said: (Tue, Aug 31, 2010 12:05:27 AM) How did you get 41/40 am not able to get that value please help me.

 Sundar said: (Tue, Aug 31, 2010 12:57:02 AM) Hi Akhila, = 1 + (5/(2 x 100) = 1 + (5/200) = 1 + (1/40) = (40 + 1)/40 = 41/40 Next step (41/40)^2 = 41/40 x 41/40 ... Hope you understand. Have a nice day!

 Sipu said: (Fri, Nov 5, 2010 09:03:29 AM) YA SUNDER IS CORRECT...

 Bala said: (Sat, Nov 13, 2010 02:33:54 AM) Its a basic thing. Where did you get 3200 in this problem?

 Manju said: (Wed, Nov 17, 2010 07:50:38 AM) Hai, where did you get from this value 3200.

 Dinesh Guptha said: (Wed, Nov 17, 2010 11:43:33 PM) I think customer deposits per year 3200. So they subtracted 3200 with that final amount it seems.

 Dinesh said: (Wed, Nov 17, 2010 11:46:28 PM) Can anyone clear me the first step.

 Venkat said: (Fri, Nov 19, 2010 10:42:07 AM) venkst:simple customer deposited twice 1600*2=3200

 Boney said: (Mon, Nov 22, 2010 07:31:27 AM) I dont understand the 2nd term in the expression Amount=1600[1+(1/2)*(5/100)]^2+ 1600[1+(5/2*100)] Amount compounded half yearly is A=P[1+r/2*100)]^2 Don't understand what this term doing 1600[1+(5/2*100)] Someone tell me

 Lavanya said: (Sun, Dec 5, 2010 09:40:35 AM) I too dint understand d first step

 Kumar said: (Thu, Dec 16, 2010 10:09:41 AM) I didn't understand someone help me.

 Anusha said: (Thu, Jan 13, 2011 04:21:34 AM) Customer has deposited twice in a year. Once in the begining i.e on Jan 1st n 2nd time on july 1st i.e after 6 months. So 1st case n=1(1 yr) & 2nd case n=1/2(half yr). So you get first and 2nd terms coresponding 2 first and 2nd case.

 Akanksha said: (Sun, Jan 23, 2011 12:10:53 PM) @ Anusha: There's nothing. See clearly, 1st january and 1st July are dates of depositions! And please someone explain why 2nd term is not squared while 1st is?

 Malkhan Meena said: (Wed, Jan 26, 2011 09:21:45 AM) On 1st january customer deposit amount and receive end of year. But in 1st july he deposit same amount (1600 Rs. ) and receive it after the same date (after 6 month). It means first he deposit for 1 year and second he deposit for 6 month. And get all amount at the end of year.

 Vishal said: (Wed, Feb 23, 2011 06:31:24 AM) Yes, its right , so in first case n (no. of years) is 1 and in second case (for july) n is 1/2 years, so now you can directly put that values in simple formula.

 Vikram said: (Fri, Feb 25, 2011 04:49:56 AM) Give the mathemetical formula for compund interest.

 Rajesh said: (Sat, Feb 26, 2011 11:37:36 PM) @Anusha: You told 2 cases one is half yearly(july) and other is yearly(jan). In yearly case the formula should be p(1+r/100)^n but they used half yearly formula only.

 Sukumar said: (Mon, Feb 28, 2011 05:09:22 AM) I can't understand [1600*41/40(41/40+1)]

 Harry said: (Sun, Mar 13, 2011 09:47:35 AM) Will someone explain the first step?

 Amit said: (Mon, Apr 18, 2011 05:12:47 AM) On 1st january customer deposit amount and receive end of year. It means first he deposit for 1 year. When interest is compounded Half-yearly: Amount = P * [ { 1 + (1/2) * (R/100) } ^ 2(n) ] Amount = 1600 * [ { 1 + (1/2) * (5/100) } ^2(1) ] = 1681 But in 1st july he deposit same amount (1600 Rs. ) and receive it after the same date (after 6 month). It means second he deposit for 6 month(1/2 year). When interest is compounded Annually but time is in fraction, say 1/2 years. Amount = P * [ 1 + { (1/2)* R/100}] Amount = 1600 * [ 1 + { (1/2)* 5/100}] = 1640 So Total = 1681 + 1640 = 3321

 Cherry said: (Tue, Apr 26, 2011 02:12:45 AM) Hi amit , c.I formula is A=p*(1+(r/100)^n) , so i understood the first step , but what s that i am expecting in the 2nd step is Amount = P * [ 1 + { (1/2)* R/100}^1/2 } , why isn't any sqrareroot included there. i mean to say u should mention the "n" i.e no. of years ass "half" right , as we are calculating only for 1/2 year , from july 1st to jan 1 st

 Leejo said: (Sat, May 14, 2011 09:07:55 AM) @Amit:gud answer

 Siri said: (Wed, Jun 1, 2011 02:40:50 PM) What is formula for simple interest?

 Priya said: (Thu, Jun 9, 2011 08:31:09 PM) Can you tell me how come it's 5 months it should be 6 month written, 1 jan to 1 july the time period is 7 month in this question they ask half yearly??

 Priya said: (Mon, Jun 13, 2011 09:10:47 AM) He deposit second time in july know. Beforre that tere are 6 months. So it is termed as half yearly. Is it clear.

 Niveditha said: (Sat, Jul 2, 2011 06:37:16 AM) Can any explain this sum fully?

 Mrudhula said: (Sun, Jul 3, 2011 03:19:23 AM) Let me explain in my point of view... Firstly... i have calculated the compound interest of 1600/- for 1year..i.e, [1600*[1+(5/100)]]=80 Then at 7th month the total amount=3200/- So the compound interest of 3200 for (1/2)year is.. [3200*[1+(5/200)]^2]=162 Now the average of 80 and 162 is.. (80+162)/2 = 121

 Prasad Shetty said: (Wed, Jul 6, 2011 12:06:41 PM) Hi Amit, you have explained the problem correctly and good thinking.

 Balaji said: (Sat, Jul 23, 2011 12:46:37 PM) Very nice amit and mrudhula.

 Satheesh said: (Sat, Jul 23, 2011 01:06:22 PM) Hi Mrudhula i think u have some logical mistakes here i will provide you the simple procedure first calculate the C.I for first 1600 in 6 months A=1600(1+5/200)^2*1/2 =1640 Now another 1600 is invested so now the total amount is 1640+1600=3240 now the C.I for this amount should be calculated i,e A=3240(1+5/200)^2*1/2 A=3321 SO HE INVESTED 3200 AND THE GAIN IS 121

 Pratik said: (Tue, Jul 26, 2011 03:45:44 PM) At the end of the page, formula is mentioned.

 Jyoti said: (Wed, Jul 27, 2011 08:52:30 AM) Hello Friends it is mentioned that bank give interest on half yearly Basis jan to june thr is 6 months cal of jan to june:1600(5)/200=40.so total is 1640. On july money become 3240 because man deposite on july. Now cal july to Dec:(3240)5/200=81. Now u can see total gain is 81+40=121.

 Anu said: (Mon, Aug 1, 2011 10:26:59 AM) Hi jyoti that was really good and simple explanation.

 Karthi said: (Mon, Aug 22, 2011 04:43:10 PM) Why putting 100*2 in denominator?

 Dinesh said: (Wed, Aug 31, 2011 03:10:21 PM) How did you get 41/40 am not able to get that value please help me.

 Ram said: (Wed, Sep 14, 2011 12:23:21 AM) First calculate CI for first deposit Jan 1st. Here interest is compounded half early So Formula is Amount = P [1 + (R/2)/ 100]^2n here n is 1 year(12mnths) so, amount is 1600[1 + 5/200]^2 and now calculate amount for money deposited on july Formula is Amount = P [1 + (R/2)/ 100]^2n here n=1/2yrs(6mnths) so, amount is 1600[1 + 5/200]^1 Add both amounts and subtract 3200(ie., 1600+1600) we get CI.

 Kapil said: (Fri, Sep 16, 2011 12:16:49 AM) Why is the rate 5% halved while calculating, once it is given that it is calculated half yearly.

 Chiranjit said: (Thu, Sep 29, 2011 09:53:47 PM) I can't understand (1+5/2*10). Please explain it.

 Anusha said: (Sun, Oct 16, 2011 02:53:55 PM) Calculate first deposit jan 1st amount= p[1+(R/2)/100]^2n here n is 1 year so amount = 1600[1+(5/2)/100]^2 =1600[1+(5/200)]^2 =1600[1+(1/40)]^2 =1600[41/40]^2 =1681. now cal amount for money deposited on july amount=p[1+(R/2)/100]^2n n=1/2 yr =1600[1+(5/200)] =1600[41/40] =1640. add both amounts 1681+1640=3321 1600 twice the customer deposited 1600*2=3200 3321-3200=121.

 Digvijay said: (Mon, Nov 7, 2011 02:31:11 PM) Thanks to anusha I was confused in second part.

 Nandhakumar said: (Sat, Nov 19, 2011 02:31:13 AM) Now only I understood. Thanks anusha.

 Santu said: (Mon, Nov 28, 2011 06:01:44 PM) Thank you. Anusha.

 Randheer said: (Fri, Dec 16, 2011 12:12:47 AM) You people might confused with the formulae and there of three formulaes where n represents exactly year i.e n=1 year, n=1/2 half year so on., Then another thing the three formulaes were having a much difference look at it as individual dont miggle those all three formulaes 2gether . Ex: to calculate half year compund intrest u shoud go with the second one don't bother about the duration here we are calculating C.I for every half yearly what ever the term it be either 1 year or 2 years u shud use the half year formulae for calculating that... look at it as very abstract.

 Amit said: (Tue, Jan 10, 2012 09:12:21 AM) CI is nothing but interest on interest. so first find SI for 1600 so SI= (1600 * 5 * 1/2)/100 = 40 now total money is 1640 after 6 month. he again deposit 1600 rs so now in july beginning total money is 1640 + 1600 = 3240 rs again find SI = (3240 * 5 * 1/2)/100 = 81 rs So total interest is = 81 +40 = 121 Rs ans.

 Shreya said: (Tue, Jan 17, 2012 03:25:01 PM) Sateesh and Jyoti gave the nice explaination.

 Saurav Karmakar said: (Sat, Jan 21, 2012 08:11:25 PM) At the time of first deposit i.e on January 1st Amount= p[1+(R/2)/100]^2(n) here n is 1 year beginning of the year so amount = 1600[1+(5/2)/100]^2 =1600[1+(5/200)]^2 =1600[1+(1/40)]^2 =1600[41/40]^2 =1681. Secondly when he deposited its July i.e after 6 months so n=half of the year=1/2 Amount=p[1+(R/2)/100]^2n n=1/2 year =1600[1+(5/200)] =1600[41/40] =1640. now add both amounts 1681+1640=3321 1600 deposited 2 times by the customer in a year therefore 1600*2=3200 gain => 3321-3200=121.

 Vishal said: (Sat, Jan 28, 2012 12:22:09 AM) Best way was shows by Jyoti.... Kudos Jyoti... :)

 Mangesh said: (Sat, Feb 11, 2012 02:39:36 PM) From 1st Jan to next 1st Jan i.e n=1(12 months) C.I.1= 1600[1+(5/2*100)]^(2*1) Now from 1st July to 1st Jan i.e n=1/2(6 months) C.I.2= 1600[1+(5/2*100)]^(2*1/2) C.I.=C.I.1 + C.I.2

 Naveenraj said: (Mon, Jun 11, 2012 03:22:38 PM) 1600 Interest 5% in 6 month (1/2 of a year) = 5/100 * 1600 * 1/2 = 40 1640 + 1600 = 3240(principal + previnterest + new deposit) 5% of 3240 in next 6 month = 5/100 * 3240 * 1/2 = 81 End of year total = 3240 + 81 = 3321 Gain = total with interest - deposit = 3321 - 3200 = 121

 Student said: (Thu, Aug 2, 2012 11:38:41 AM) FV=P(1+r/n)^(nt) FV = Future value of the deposit. P = Principal or amount of money deposited. r = Annual interest rate (in decimal form). n = Number of times compounded per year (1 or 2 or 3... etc). t = Time in years for which the money has been deposited. Use this formula and you will get the answer.

 Vivek Kumar said: (Mon, Oct 29, 2012 03:29:07 AM) Can someone tell me why have they considered 1600 value for the next 6 months (P) should be 1600 + Interest for the next half.

 Pankaj Parashar said: (Fri, Dec 21, 2012 11:34:14 PM) According to me itis given that compounded half yearly So rate=5/2=2.5% So first 6 months ci=1600*2.5/100=40 Now amount=1600+40=1640 Now 2nd 6 months ci=3240*2.5/100=81 So total ci = 80+40 = 121.

 Zaid Junaid said: (Fri, Feb 15, 2013 04:50:26 PM) Well according to me it means that he is depositing the amount 2 times first in Jan and than in July. So for Jan years will be 1 but for July it will be 1/2 years. So that's why the second term has not been squared.

 Suresh said: (Wed, Feb 27, 2013 03:39:01 PM) Well. Is there any shortcuts to solve the problem?

 Arvind said: (Sat, Mar 23, 2013 09:45:20 AM) Hi. Can someone please let me know why the 2nd time of deposit been multiplied by 2*100 (in denominator). As per my understanding the period is only 6 months in this case hence the time period is 1 and so is the case with the interest right we don't have to multiply it with 2 as only for 6 months. Kindly clarify why the denominator is multiplied with 2?

 Nil.Dhongde@Gmail.Com said: (Tue, Apr 2, 2013 11:12:02 PM) My gosh. So many comments. I know it is bit confusing and I too. Let me try to make you understand. So here we start. you might have familiar with the formula, C.I = p[1+(R/100)]^n. Here p = principal amount. R = rate. n = no.of years. But in the problem we are dealing with half year. Means we are getting C.I on 6 months * we have given annual rate of 5%. So for half year it would be R/2 * As we are calculating C.I over every 6 months, so for a year n become 2 (as two half year is equal to one year). So here n = 2. So our formula becomes, C.I = P[1+(R/2*100)]^2. Here p is given as 1600 Rs. Now after 6 months, on date 1 July another amount of 1600 Rs got deposited. So again we have to calculate the C.I for this amount for a 6 months only(upto 31 Dec) so that we can get the C.I from Jan 1 to July 1 and from July 1 to Dec 31. So as to complete one year. as We are asked about C.I over total one year. So, For a second amount formula for C.I becomes, C.I = P[1+(R/2*100)]^1. Combining two we have, C.I = P[1+(R/2*100)]^2 +P[1+(R/2*100)]^1.

 Pooja said: (Sun, Apr 7, 2013 08:05:38 PM) @Amit: Thanks a lot you made me understand the concept. It took me whole day to ponder over the 2nd half of the expression.