# 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

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

A) Rs.9000 | B) Rs.9002 |

C) Rs.9200 | D) Rs.9120 |

Explanation:

Required Money = P.W of Rs. 10028 due 9 months hence

= Rs.[10028 x 100] / [100+(12 x 9/12)] =Rs.9200

A) 700 | B) 760 |

C) 768 | D) 786 |

Explanation:

P.W = (100 x T.D)/(R x T) = (100 x 168)/(14 x 2)= 600

Sum = (P.W + T.D) = Rs. (600+ 168) = Rs.768.

A) Rs. 600 | B) Rs. 768 |

C) Rs. 878 | D) Rs. 668 |

Explanation:

We know that,

P.W = 100×T.D/R×T

= 100×168/14×2

P.W = 600.

Now, required Sum = (P.W. + T.D.)

= Rs. (600 + 168)

= Rs. 768.