Aptitude - Compound Interest - Discussion

On 1st january customer deposit amount and receive end of year.

But in 1st july he deposit same amount (1600 Rs. ) and receive it after the same date (after 6 month).

It means first he deposit for 1 year and second he deposit for 6 month. And get all amount at the end of year.

Yes, its right , so in first case n (no. of years) is 1 and in second case (for july) n is 1/2 years, so now you can directly put that values in simple formula.

Give the mathemetical formula for compund interest.

@Anusha:

You told 2 cases one is half yearly(july) and other is yearly(jan). In yearly case the formula should be p(1+r/100)^n but they used half yearly formula only.

I can't understand

[1600*41/40(41/40+1)]

Will someone explain the first step?

On 1st january customer deposit amount and receive end of year. It means first he deposit for 1 year.

When interest is compounded Half-yearly:

Amount = P * [ { 1 + (1/2) * (R/100) } ^ 2(n) ]
Amount = 1600 * [ { 1 + (1/2) * (5/100) } ^2(1) ] = 1681


But in 1st july he deposit same amount (1600 Rs. ) and receive it after the same date (after 6 month). It means second he deposit for 6 month(1/2 year).

When interest is compounded Annually but time is in fraction, say 1/2 years.

Amount = P * [ 1 + { (1/2)* R/100}]
Amount = 1600 * [ 1 + { (1/2)* 5/100}] = 1640

So Total = 1681 + 1640 = 3321

Hi amit , c.I formula is A=p*(1+(r/100)^n) , so i understood the first step , but what s that i am expecting in the 2nd step is Amount = P * [ 1 + { (1/2)* R/100}^1/2 } , why isn't any sqrareroot included there. i mean to say u should mention the "n" i.e no. of years ass "half" right , as we are calculating only for 1/2 year , from july 1st to jan 1 st

@Amit:gud answer

What is formula for simple interest?