Aptitude - Compound Interest - Discussion

@All

It's simple;

5% of 1600 is 80.
as it is for a year, take half of 80 and add to 1600 become 1640,
Now add 1640 and 1600 from July to Dec, it becomes 3240,
Take 5%of 3240 which is 162.
As it is for the year take half of 162 which is for 6 months which becomes 81
Now add 40 and 81 which become 121.

@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.

On 1st January he deposited 1600.

Using the formula of compound interest half yearly
A=P(1+(R/2/100))²n.

n is 1/2 here as he deposits for 6 months i.e, till July.
Now, A=1600(1+(5/200)^2*.5
A = 1600 * 1.025,
= 1640.

Therefore compound interest = 1640 - 1600,
= 40.

Now in July he deposits 1600.
So, the principal amount becomes 1640 + 1600 = 3240.

So, using the formula
A=3240*(1+5/200)^2*0.5
A=3240*1.025,
= 3321.

Therefore, compound interest is 3321 - 3240 = 81

Total compound interest is 40 + 81 = 121.

BANK INTEREST - 5%.

1st jan deposit = 1600.
1st jul deposit = 1600.

1st Jan = 1600 * 5/100 = 80.
For 6months 80/2v= 40.
40 + 1600 = 1640.
1st july = 1640(jan) + 1600(jul) = 3240.
3240*5/100v= 81.

= 40+81 = 121.

Normal CI's amount formula :
A= P[ 1+ R/100]^n.

When compounded half-yearly :
A= P[1+(R/2)/100]^2n.

Guys.

Let's solve this in the traditional method.

Interest for first deposit
1600 * 25/1000 = 40.

Interest for second deposit + the amount for first deposit (intrest + deposit amount)
3240 * 25/1000 = 81.

Now adding both intrest we get 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.

So, basically the person is depositing the amount of 1600 in 1st Jan and again the amount of 1600 in 1st July.

So, Customer deposit = 1600 + 1600 => 3200.

Now, using Simple interest formula cal the 1st jan deposit SI.
SI = 1600(5)(1)/100(2).
Si = 40.
AMOUNT = 1600 + 40 => 1640 ---> Eq 1
SI for 1st July with same process but this time the principal will be P = 1640.
SO, SI = 41 and;
AMOUNT will be = 1640+41 => 1681 ---> Eq 2.
ADD BOTH Eq 1 and Eq 2 we get =>3321.

CI = customer deposit - amount.
CI = 3321 - 3200.
CI = 121.
HOPE YU GET IT.

But why they didn't take 2t for next half year? please explain to me.

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.