Aptitude - Compound Interest - Discussion

Amount after 1 year on Rs. 1600 (deposited on 1st Jan) at 5% when interest calculated half-yearly.
=P(1+(R/2)100)2T=1600(1+(5/2)100)2*1=1600(1+140)2

Amount after 1/2 year on Rs. 1600 (deposited on 1st Jul) at 5% when interest calculated half-yearly.
=P(1+(R/2)100)2T=1600(1+(5/2)100)2*12=1600(1+140)

Total Amount after 1 year.
=1600(1+140)2+1600(1+140)=1600(4140)2+1600(4140)=1600(4140)[1+4140]=1600(4140)(8140)=41*81=Rs. 3321.

Compound Interest = Rs.3321 - Rs.3200 = Rs.121.

1st 6th month (1jan to 1 July) (half-yearly basis) Rate of intrest=R/2 and R = 51.
Then interest =1600 X 5/2 X 100=>40.

Amount of 1st 6th Month = 1600(principal) + 40(interest) => 1640.
Same for july to dec now P=1640 and R = 5/2.
Then intrest =1640 X 5/2 X100==>41.

Amount of 2nd 6th Month=1640(principal)+41(interest)=>1681
then total amount with intrest = 1640+1681;
= 3321;

Toal amount gained = 3321 - (1600+1600).
= 121;

SI : 625 x 4% x 2yr = ---------------------------------- 50.00.
CI : 625 x 4% x 1st Yr ------------------ 25.00.

(625+25) x 4% x 2nd yr ------------- 26.00.
          ------      -------
Total    51.00    50.00.

Difference between SI & CI (51.00 - 50.00) 1.00.

For 1/2 year formula is =P(1+(R/2)/100)^ 2n.
Now 1600 for 1st 1/2 year or 6 months so n=1/2.
=1600(1+(5/200)^1 = 1640.

This money bank won't returns him on July 1st it is kept in the bank till December. So from July to December 1640 also carries interest again apply formula for this with n=1/2
we get 1681 here 81 is the interest he got.

On July again he deposits 1600 again apply formula we get 1640 40 is the interest so total interest 81+ 40 = 121.

First, Deposit
Principal Amount (P1): 1600.
Rate of Interest (R): 5.
Frequency of Compounding(N): 2.
Tenure Period(T): 0.5.
Compound Interest (CI): 40.
Compound Amount (CA): 1640.

CA = 1600*(1 + 0.05/2)^1.
CA = 1640.

Second Deposit, 1600
Now, for the rest of the tenure we will be investing.. CA of first deposit + second deposit.

1640 + 1600 = 3240 (P2).
CA = 3240*(1 + 0.05/2)^1.
CA = 3321.

CI = CA - P.
CI = 3321 - (1600+1600).
CI = 121.

If time period is T and the rate R.
for half yearly basis calculation;
T`=2T. And. R`=R/2.

Here total period=12 month= 1 year,
Rate= 5%.
T`=2. R`= 2.5.

For the first half,
1600 × 2.5/100 = 40,
CI = 40 × 2 = 80,

For second half
P = 1640 × 2.5/100 = 41.
CI = 41×1 = 41,
Total CI = 121.

Note.
For 2 year CI calculation
Multiple is 2,1.

For 3-year CI calculation
Multiple are 3,3,1.
For 4 year CI calculation
Multiple are 4,6,4,1.

@All.

Guys we can do this in an easy way listen;

Firstly, from 1st Jan to July we give 1600 to the bank
1600*5/100*1/2(1/2 because it's on half yearly based)
So, the answer is 40.

After that from July to December the process will be the same but now the ci will be on 1640
1640*5/100*1/2 answer is 41.

Now we have 1600 in July so the amount will be;
1600*5/100*1/2.
40.

So, the total interest is 40+41+40 is equal to 121.

Guys most of you might be confused with the formula, lets do this way:

1st 6 months deposit = 1600,

Interest earned at 5% upto July = (1600 x 5/100 x 1/2) = 40.

Note: In compound interest interest gets added to the principle.

So P = 1640 now, and next deposit in July = 1600.

Total deposit = (1640+1600), interest = (3240 x 5/100 x 1/2) = 81.

Total profit earned as interest = 40+81 = 121.

Hope this helps.

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.

We can also solve it by basic SI formula.
PNR/100.

Customer deposits 1600 twice in a year.
In a first 1/2 yr,p=1600,n=1/2,r=5%,
interest is..1600x1x5 / 2x100 = 40,
In a second 1/2 yr, p becomes 1640,
Interest=1640x1x5 / 2x100 =41,
So interest gained by amount deposited on;
January at the end of yr=81,
And,1600 is deposited on july,again same procedure.
I = 1600 x 1 x 5/2x100 = 40.
So, 81 + 40 = 121.