True Discount Questions

FACTS  AND  FORMULAE  FOR  TRUE  DISCOUNT  QUESTIONS

Suppose a man has to pay Rs.156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to Rs. 156 in 4 years. So, the payment of Rs. 100 now will clear off the debt of Rs.156 due 4 years. Hence, we say that :

Sum due = Rs.156 due 4 years hence;

Present Worth (P.W) = Rs. 100;

True Discount (T.D) = (Sum due) - (P.W)=Rs. (156 - 100) = Rs. 56

We define : 

               T.D = Interest on P.W  

               Amount = (P.W) + (T.D)

Interest is reckoned on P.W and true discount is reckoned on the amount.

IMPORTANT FORMULAE

Let rate = R% per annum and Time = T years. Then,

1. $P.W=\frac{100\times Amount}{100+\left(R\times T\right)}=\frac{100\times T.D}{R\times T}$

2. $T.D=\frac{\left(P.W\right)\times R\times T}{100}=\frac{Amount\times R\times T}{100+\left(R\times T\right)}$

3.  $Sum=\frac{\left(S.I\right)\times \left(T.D\right)}{\left(S.I\right)-\left(T.D\right)}$

4. (S.I) - (T.D )= S.I on T.D

5. When the sum is put at compound interest, then 

$P.W=\frac{Amount}{{\left(1+{\displaystyle \frac{R}{100}}\right)}^T}$