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.

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

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

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.

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.

Amount after 1 year on Rs 1600 (deposited on 1st. Jan)
= 1600(1+5/2100)^(2*1)=1600(41/40)^2,
= 1681.

Compound interest
= 1681 - 1600
= 81.

Amount after 12 year on Rs 1600(deposited on 1st Jul)
= 1600(1+5/2100)^(2*(1/2))
= 1600(41/40)
= 1640

Compound interest
=1640 - 1600 = 40.

Required gain;
= 81 + 40,
= 121.

1600* 5/100=80.
For 6 month : 80/2= 40
3200+40(including previous)=3240*5/100=162. For the next 6 month, the value will be 81.
Now we have to add 40 + 81.

How it's come 5/2*100 because r is 5% only? Explain please.

Yes right, Thanks @Amazu.

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.

So in the question, they have given that compounded half-yearly (1 year = 12 months) so we have to calculate for every 6 months.

First, let us understand the difference b/w simple interest and compound interest.

In Simple interest, the interest after a year will not be added to the principal (sum) amount.

Whereas compound interest. The interest after a year will be added to the principal (sum) amount.

So calculating for the first 6 months using formula S. I = PTR/100. Here 6 months to covert in to years just divide by 12. (in first 6 months TIME in years = 6/12).

S.I = (1600* 6/12*5) / 100.

S.I = 40.

AS I have mentioned this interest will be added to PRINCIPAL since we are calculating for Compound Interest.

So, 1600 + 40 = 1640 this is for 6 Months.

GIVEN ====> in July he again invest 1600 so total will be 1640+1600 = 3240.

We have to calculate for another 6 months.

Here the PRINCIPAL WILL BECOME NEW PRINCIPAL ====== 3240.
S.I = PTR/100 ==> (3240*6/12*5) /100 ==> 81.

This will be again added to the last Principal to obtain ANOTHER NEW PRINCIPAL SO.

3240+81 = 3321.
The total amount deposited is 3200.
3321-3200 = 121.

I hope this info will be helpful.

Thank you.