Aptitude - Compound Interest - Discussion
Discussion Forum : Compound Interest - General Questions (Q.No. 1)
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:
Answer: Option
Explanation:
| Amount |
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| = Rs. 3321. |
C.I. = Rs. (3321 - 3200) = Rs. 121
Discussion:
220 comments Page 4 of 22.
Satheesh said:
1 decade ago
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
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
Bikash Mahato said:
3 years ago
On 1st Jan Rs. 1600(P1)amount is deposited, the CI Amount is(Int1): P(1+R)^n-P => 1600(1+5/(2 * 100)) - 1600 = Rs. 40.
On 1st July Rs. 1600 (P2) amount is added, current total amount = Rs. 1600(P1) + 40(CI) + 1600(P2) = Rs. 3240.
Again CI amount (Int2) (with R=5%, N=1/2 years) = 3240(1+5/(2 * 100))-3240 = Rs. 81.
Total Interest Amount = Int1 + Int2 => 40 + 81 = Rs. 121.
On 1st July Rs. 1600 (P2) amount is added, current total amount = Rs. 1600(P1) + 40(CI) + 1600(P2) = Rs. 3240.
Again CI amount (Int2) (with R=5%, N=1/2 years) = 3240(1+5/(2 * 100))-3240 = Rs. 81.
Total Interest Amount = Int1 + Int2 => 40 + 81 = Rs. 121.
(14)
Cherry said:
1 decade ago
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
Anusha said:
1 decade ago
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.
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.
Rana suresh varma said:
8 years ago
1st calculate CI on 1600 half yearly for one year so 1600(1+5÷200)^2.
= 1600(205÷200)(205÷200),
= 1681,
= CI = 1681-1600 = 81->eqn1.
Next calculate CI on 1600 which is deposited after 6 months i.e. for 6 months.
= 1600(1+5÷200),
= 1600(205÷200),
= 1640.
= CI is = 1640-1600= 40->eqn2.
Add eqn1 and eqn2 we get;
= 81 + 40 = 121 this is the gain.
= 1600(205÷200)(205÷200),
= 1681,
= CI = 1681-1600 = 81->eqn1.
Next calculate CI on 1600 which is deposited after 6 months i.e. for 6 months.
= 1600(1+5÷200),
= 1600(205÷200),
= 1640.
= CI is = 1640-1600= 40->eqn2.
Add eqn1 and eqn2 we get;
= 81 + 40 = 121 this is the gain.
Arvind said:
1 decade ago
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?
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?
Anubhab said:
8 years ago
@Sam.
As we know when interest is compounded half-yearly, we divide the rate by 2 and multiple the year(n) by 2.
As he deposits in Jan and bank gives interest half yearly so there so by the next year Jan there will be 2 r% interest which is the reason why n=2 and for the deposit in July he gets the only one which is the reason n=1.
Hope it helped.
As we know when interest is compounded half-yearly, we divide the rate by 2 and multiple the year(n) by 2.
As he deposits in Jan and bank gives interest half yearly so there so by the next year Jan there will be 2 r% interest which is the reason why n=2 and for the deposit in July he gets the only one which is the reason n=1.
Hope it helped.
VINOD said:
8 years ago
CI CAN BE EXPRESSED IN TERMS OF SI.
IN THIS PROMBLEM,
FOR FIRST 6 MONTHS CALCULATE SI OF PRINCIPAL SINCE CI CALCULATED ON HALFYEARLY BASIS.
SI FOR 6 MONTHS = (1600 * (1/2)*5)/100 = 40.
CI FOR NEXT 6 MONTHS = (1600+40) * (1/2) * 5)/100 = 41,
TOTAL CI = 40 + 41 = 81.
SI FOR 6 MONTHS FROM JULY = (1600*(1/2)*5)/100 = 40,
TOTAL EARNING = 40 + 81 = 121.
IN THIS PROMBLEM,
FOR FIRST 6 MONTHS CALCULATE SI OF PRINCIPAL SINCE CI CALCULATED ON HALFYEARLY BASIS.
SI FOR 6 MONTHS = (1600 * (1/2)*5)/100 = 40.
CI FOR NEXT 6 MONTHS = (1600+40) * (1/2) * 5)/100 = 41,
TOTAL CI = 40 + 41 = 81.
SI FOR 6 MONTHS FROM JULY = (1600*(1/2)*5)/100 = 40,
TOTAL EARNING = 40 + 81 = 121.
Mahesh said:
8 years ago
1600 initial amount, we get 40 interest. So total money 1st 6 months is 1640 this money will not be returned, it again carries for next 6 months to calculate interest at the end of December. Again 1640 apply formula we get 1681. We can use common sense to calculate interest for 1640 (1600+40).
We know for 1600 40 interest for 40? Which is 1 rs.
We know for 1600 40 interest for 40? Which is 1 rs.
Nitesh Kumar said:
6 months ago
@All.
Here, is my explanation for the answer.
Basically in question, there is not mention the rate if for a year,
If the rate is given for the year then for half a year the rate becomes 2.5%,
Then 1600's 5 % is 80 then half is 40 means 2.5% of it,
Then next 6month 1600 + 40 '5% is 162 so 2.5 is 81 then total;
Interest he earn is 40 + 81 = 121.
Here, is my explanation for the answer.
Basically in question, there is not mention the rate if for a year,
If the rate is given for the year then for half a year the rate becomes 2.5%,
Then 1600's 5 % is 80 then half is 40 means 2.5% of it,
Then next 6month 1600 + 40 '5% is 162 so 2.5 is 81 then total;
Interest he earn is 40 + 81 = 121.
(8)
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