Aptitude - True Discount - Discussion

Hey Guys... I am little worried about this solution. Let me put my thoughts below.
Cash = 12000 Today
Interest rate 18% /Annum.
After 8 Months Interest will be 12000*(8*18%/12)= 1440.

If I will not pay 12000 now , then my worth will be 12000+1440 = 13440.
If I pay 12800 after 8 months, still I will have 13440-12880= 560 in my hand.

If I pay 12000 now, then I cant have 560 in my hand which is a interest from this cash.

So I feel 12880 after 8 months is best answer.

The question here asks which option is better for owner of the scooter.
So by explanation of Madhu.T cash is better than credit.

Because if we take cash now and give it for interest we get 1440 after 8 months at 18% interest per annum. But if we accept credit we only get 880 after 8 months.

Just see my ans:-
By taking after 8 months how much we will get excess money
= 12880-12000 = 880/- ..........(Pls remind this),

If we take cash 12000/- now it self the interest would be after 8 months @ 18% P.A

= 12000*(18/100)*(8/12)
= 1440

so instead of going for credit, cash is better.

Thank you @Madhu for the best explanation you gave. @Deepak, this deal is for a dealer not for the customer.

For the customer, the best one is of 12880. Otherwise, he'll charge with an imaginary amount of 13440.

And for the dealer, the best one is of 12000 in cash.

The question is which one is a better option for the seller not for the buyer, so if he sells it for cash of Rs. 12000 but if he sells for credit he will only receive only Rs. 11500 (solved using formula).

Hence better option is to sell it for cash.

S.I= (P*T*R)/100.
for P=12000,

S.I = 1440,
Total amount = P+S.I = 13440.
for what present value of P,
The total amount will be=12880 after 8 months with 18% interest is calculated using the formula
P.W= (P * 100)/ 100+ (R*T).

Amount= P.W + I.

I = (P.W * T * R)/100.

So,

A = P.W+ (P.W * T * R)/100.

100(A) =100 * P.W + P.W * T * R.

P.W = 100A/100 + T * R.

A = 12880 (A is the total amount obtained after 8 months).

12000 -> obtained P.W.

P = A/(1 + nr).

Where:
P = The present value of the amount to be paid in the future,
A = The amount to be paid,
r = The interest rate,
n = The number of years from now when the payment is due.

After 8 does not mean in 4 months as the previous question. The question does not say that in 8 months but after 8months starting from 4 left months of the year the man will start to pay right?

Hi Tanu
As per formula of Present Worth (P.W)

100 x Amount/100 + (R = Rate perannum x T = Time Year)

12000 is better as such 12880 is due amount after 8 Months

=100+18*8/12
= 100+12
=112