Aptitude - Compound Interest - Discussion

I dont understand the 2nd term in the expression
Amount=1600[1+(1/2)*(5/100)]^2+ 1600[1+(5/2*100)]
Amount compounded half yearly is A=P[1+r/2*100)]^2
Don't understand what this term doing 1600[1+(5/2*100)]
Someone tell me

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.

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.

@ALL.

You all are facing problem because you are obsessed with "n" to substitute as "year" always.
"n" is basically how many "times" rate is applied on amount.

Here, it is clearly given that the interest is calculated on "half-yearly" basis. Now because of half yearly basis.

Here "n" will be "1" for 6 months (and r=r/2).
and "n" will be "2" for 1 year ( and r=r/2).

Suppose if it was given quarter-yearly,
"n" would be "1" for 3 months ( and r=r/4).
"n" would be "2" for 6 months (and r=r/4).
"n" would be "3" for 9 months (and r=r/4).
"n" would be "4" for 1 year (and r=r/4).

So, this guy kept his first 1600Rs amount for " two period" time.
that is, from 1st jan to 30th June (1st period) and from 1st July to 31st Dec (2nd Period).
he also deposited another amount on 1st July, this amount is kept for "one period".

That is, from 1st July to 31st Dec.

Therefore there is square(n=2) in a first Formula and no square(n=1) in a second formula.

Hope I helped little bit.

@Gouthami.

How 1600 becomes 3240?

Please explain it.

@Amit.

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

Anyone, please give a clear explanation about the given formula.

Why is it used? Please elobarate.

If time period is T and the rate R.
for half yearly basis calculation;
T`=2T. And. R`=R/2.

Here total period=12 month= 1 year,
Rate= 5%.
T`=2. R`= 2.5.

For the first half,
1600 × 2.5/100 = 40,
CI = 40 × 2 = 80,

For second half
P = 1640 × 2.5/100 = 41.
CI = 41×1 = 41,
Total CI = 121.

Note.
For 2 year CI calculation
Multiple is 2,1.

For 3-year CI calculation
Multiple are 3,3,1.
For 4 year CI calculation
Multiple are 4,6,4,1.

How did you get 41/40 am not able to get that value please help me.

Hi Akhila,

= 1 + (5/(2 x 100)

= 1 + (5/200)

= 1 + (1/40)

= (40 + 1)/40

= 41/40

Next step (41/40)^2

= 41/40 x 41/40
...

Hope you understand. Have a nice day!