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:
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.
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.
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
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.
Annie said:
(Wed, Dec 7, 2011 08:22:31 PM)
The question is for one year. What if 5 years? please help me. I've got headache thinking about this topic.
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?
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.
C.I. = Rs. (3321 - 3200) = Rs. 121