Aptitude - Compound Interest - Discussion

Why does the second part not have a square i.e ^2 for it?

From where did 3200 came?

I got 123, How that's possible?

Most helpful for banking. Thanks to all friends.

PRINCIPLE AMT p=1600RS. THIS AMOUNT IS COMPOUNDED HALF YEARLY SO r=5/2%.

Time= 2t this is theory based on the amount calculated half yearly.

For the first six months he received an interest we calculate as follow.

= p (1 + r/100) ^2t.

Here t = 6 month since we have to put it in the formula as a year so 6 month means 1/2 year.

So compound interest for 6 month = 1600 (1 + 5/2 * 100) ^2 * 1/2.

= 1600 (1 + 5/200) =1640 this is the amount he has in his account after six months.

Again bank gives him six-month interest on this amount after the completion of first six months now understand clearly after the six-month interest will be given on 1640 so this is principle amount for the bank again follow the above procedure.

= 1640 (1 + 5/2 * 100) ^2 * 1/2.
= 1640 (1= 5/200) =1681.

The total amount he received at the end of year = 1640 + 1681 = 3321.

Total amount he paid = amount paid for first six month + amount paid for next six month = 1600 + 1600 = 3200.

Interest he received at the end of 12 month = 3321 - 3200 = 121.

Why the amount of first six months is not included with 1600 as principal while calculating the amount of next six months?

Thanks @Amit, @Jyoti and @Nil.Dhongde.

I don't understand how come it is divided by 200? What is 200?

And isn't the formula P(1+i)^n?

If interest is 5% compounded semi-annually. Then what is the effective interest for 1st half, is it 5/2% or 5%?

Here is a very simple method.

1600 * 5 * 1/2 * 100 = 40.

Now the amount you have on 1st July is 1600 + (1600 + 40) = 3240.

So.
3240 * 5 * 1/2 * 100 = 81.
Now add 40 + 81 = 121.