Aptitude - Compound Interest - Discussion

I did not understand the first calculative statement please help me.

Why [1600 x (1 + 5/2 x 100 )] this step is taken after the half-yearly count?

If haf yearly then n=2n and if for 2years then n=2n.

Hi, I don't understand how you set up the calculations in that way. The formula is fv=pv (1+r) n. Aren't the calculations suppose to be fv=1600 (1+0.05)1?

@ALL.

P (1+ R/2 /100) ^ 2n for half yearly.

P (1+R/100) ^n for yearly.

Don't think about the second 1600 deposited on july 1st, forget this completly to avoid confusion.

1600 first deposit becomes 1640 at the June end (use half yearly formula).

Since this is not given back on June end it will remain in the bank.

So what we think is, 1600 is kept for 6 +6 months = 1 year and we use yearly formula. (completely mistaken).

How can we use yearly interest formula when question clearly says interest calculated half yearly.

If we use yearly formula we get 1600 (1+ 5/100) ^1 =1680.

Now see when half yearly formula is used.

1600 (1+ (5/200) ) check half yearly formula.

Which gives 1640.

As I said this 1640 not given back, again apply half year formula.

1640 (1+5/200) = 1681.

So interest is 81.

Compare the interest you got using yearly formula (mistaken formula) and actual formula (correct formula). We got 80 (mistaken) and we got 81 (correct) see the difference.

So it is used p (1+ R/2 /100) ^2n = 1600 (1+ 5/200) ^2 = 1681 correct n= 1/2 +1/2 =1.

1600 initial amount, we get 40 interest. So total money 1st 6 months is 1640 this money will not be returned, it again carries for next 6 months to calculate interest at the end of December. Again 1640 apply formula we get 1681. We can use common sense to calculate interest for 1640 (1600+40).

We know for 1600 40 interest for 40? Which is 1 rs.

For 1/2 year formula is =P(1+(R/2)/100)^ 2n.
Now 1600 for 1st 1/2 year or 6 months so n=1/2.
=1600(1+(5/200)^1 = 1640.

This money bank won't returns him on July 1st it is kept in the bank till December. So from July to December 1640 also carries interest again apply formula for this with n=1/2
we get 1681 here 81 is the interest he got.

On July again he deposits 1600 again apply formula we get 1640 40 is the interest so total interest 81+ 40 = 121.

Half yearly formula is used in which for case 1: (of january) n=1;.

Half yearly formula is used in which for case 2: (of july) n=1/2(6 months);

I think the first step is evaluated as follows:
That square term came from the half-yearly basis.

We have given for half year but we need to find for a full year. So we set n=2 (That is twice of half year) and n=1 for next case (half year).

Can someone explain me?

If I don't go for formula.. so let's do with normally.

January to july,
Principal-1600
rate-5%
time-1 (i.e half year)

so CI= 1600*0.05*1
= 80.
Hence the amount is 1600+80=1680 which is the principal for the second time.

Now July to December,

His new principal=1680 and he deposit 1600 more so his new principal is 1680+1600=3280.
rate is same = 5%
time=1 (half yearly)

So CI = 3280*0.05*1.
= 164.

So its 164. How 121? Please correct me.

Shortcut method.

Total ci =5+2.5+(5*2.5/100)
=7.6%.

ci=7.6 of 1600=121.