Aptitude - Compound Interest - Discussion

@Amit.

1 year formula is p(1+R/100) ^n.

Hello all,

My solution:

First calculate Amount for money deposited in 1st Jan for half year.

n=1/2 R=5 P= 1600.
Amount = P(1+(R/2)/100)^2n ------> (Formula when interest compound half-yearly)
=1600(1+(5/2)/100)^2/2,
=1600(1+5/200),
=1640.

Now we will add the amount 1640 into money deposited in 1st July.
1640+1600 = 3240.
Now P=3240 and will calculate amount for the remaining half year.
P=3240 R=5 n=1/2.
Amount = P(1+(R/2)/100)^2n.
= 3240(1+(5/2)/100)^2/2
= 3240(1+5/200)
= 3321.

Total amount deposited =1600 + 1600 = 3200.
Amount gained = 3321 - 3200 = 121.

Hope this helps

Good, thanks @Mohsin Khan.

Thanks @Mohsin Khan.

Well explained @Satheesh.

1st 6th month (1jan to 1 July) (half-yearly basis) Rate of intrest=R/2 and R = 51.
Then interest =1600 X 5/2 X 100=>40.

Amount of 1st 6th Month = 1600(principal) + 40(interest) => 1640.
Same for july to dec now P=1640 and R = 5/2.
Then intrest =1640 X 5/2 X100==>41.

Amount of 2nd 6th Month=1640(principal)+41(interest)=>1681
then total amount with intrest = 1640+1681;
= 3321;

Toal amount gained = 3321 - (1600+1600).
= 121;

@ALL.

An explanation for why there is square in 1 st term in amount.

As there is square in first term amount indicating the duration because the CI given here is the half-yearly basis not yearly so from,

1 st Jan -1st Jan(next year)=1 year =2 half year.n=2
1st Jul- 1st Jul(next year)=6 months=1 half-year ie.n=1

@Gouthami.

How 1600 becomes 3240?

Please explain it.

Simple trick: firstly for the half-year rate of interest would be half that is 2.5%.
2.5%of 1600 = 40.

This is compounded 1640 and again deposited another 1600 it becomes 3240.
Now 2.5%of 3240 = 81.
Finally, 81+ 40 = 121.

A = P (1 + r/n) ^nt.

A = Final amount.
P = Initial principal balance.
R = Interest rate.
N = Number of times interest applied per time period.
T = Number of time periods elapsed.