Aptitude - Compound Interest - Discussion

@Mon Doley.

Thanks, you done a great job.

Still in confusion, Check out these:

According to question Rs. 1600 is invested twice. i.e. from 1st Jan to till the end of the year, and from 1st July to the end of the year.

So we have -.

P= Rs. 1600; R = 5%; N1= 1yr; N2= 1/2yr.

So, Amount->1 = p{1+ (R/2) /100}^2 * N1, ie CI calculated half yearly.

= 1600 (1 + 5/200) ^2 * 1.
= 1600 (205/200) ^2.
= 1600 (41/40) ^2.
= 1600 * 41 * 41/40 * 40.
= 41 * 41 = 1681 --->(i).

And,
Amount->2 = p{1 + (R/2) /100}^2 * N2.

= 1600 (1 + 5/200) ^2 * 1/2.
= 1600 (1 + 5/200).
= 1600 (41/40).
= 40 * 41.
= 1640 ----> (ii).

Therefore Total Amount:

(i) + (ii) = 1681 + 1640 = 3321 Rs.

As the same amount, 1600 is invested twice so Total principal = 1600 * 2 =3200.

Therefore, C.I = Amount - Principal.

= 3321 - 3200.
= Rs. 121.

Where the present value (pv) = 1600.

Rate: 5%/2.

Then, n:2 for 1st jan to dec and 1 for 1st jul to dec.

Therefore fv =1600 (1 + 0.025) ^2 + (1 + 0. 025).

= 1600 * 2. 07563.

= 3321.

Now the amount he would have is 3321 - 3200 = 121Rs.

It is very easy to solve without formula.

Such as 1600 *.05 = 80/2 =40.
So, 1640 *.05 = 82/2 = 41.
So that interest = 81 and 1600*.05 = 40
Then Ans = 81 + 40 = 121.

Thank you @Amit. Your explanation is simple to understand the concept.

I solve this by the simple interest method.

Where p = 1600, r = 5, T = 0.5(6 months) (January amount).
Interest = (1600*5*0.5)/(100*2) = 40 Rs.

Now p =1640(January) + 1600(newly added in July).
So, p = 3240, r = 5, t = 0.5(6 months).
Interest = (3240*5*0.5)/(100*2) = 81 Rs.

Now the total interest = 40 Rs + 81 Rs =121 Rs.

Thank you all those helped me to clear the problem.

For half yearly basis (R) = 5/2 = 2.5%.

(2.5% of 1600)/100 = 1600*2.5. = 40

Customer has rs 1600 + 40 = 1640.

He again adds 1600 on 1st July so 1600 + 1640 = 3240.

(2.5% of 3240)/100 = 3240*2.5 = 81.

Therefore, total interest earned is 81 + 41 = 121.

5/2 (since half yearly, had it been quarterly 5/4 or monthly 5/12).

= 2.5 => 100 + 2.5 = 102.5 => 102.5/100 = 1.025.

For 1st amount = 1600 * 1.025 * 1.025 = 1681.

For 2nd amount = 1600 * 1.025 = 1640.

Therefore interest earned 81 + 40 = 121.

How come 81/40? Can any one explain?