Aptitude - Compound Interest - Discussion

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.

Can someone tell me why have they considered 1600 value for the next 6 months (P) should be 1600 + Interest for the next half.

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.

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.

Well. Is there any shortcuts to solve the problem?

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.

@Amit: Thanks a lot you made me understand the concept. It took me whole day to ponder over the 2nd half of the expression.

Let me try to make you understand.

>> First 6 months .

* Deposit is 1600.

* Interest is 5% half yearly.

So, Interest is 5/100 for 6 months,

i.e., one year is represented as 1 (one).

Half yearly means 1/2 (six months), {quarterly 1/4 (4 months each) for example}.

To calculate interest on deposit.

>> deposit * interest * years.
>> 1600 * 5/100 * 1/2.
>> 40.

Interest on 1600 is 40,
So 1600 + 40 = Rs. 1640.

After first six months, the total amount available is 1640.

>>> Next Six months.
>> Deposit is 1600.

So, Total available balance is 1600 + 1640(from first 6 months).

>> 3240 * (5/100) * (1/2).
>> 81.

Finally, So total interest is 40 + 81 = 121.

As it is half yearly basis,

The formula is A=p[1+(R/2)/100]^2(n).

But here only time varies i.e n=1y & n=1/2y.

Now substitute.