## True Discount

### What is true discount

suppose a man who 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.)=Rs.(156-100)=Rs .56=( Sum due )-(P .W.)

We define: T.D. = Interest on P.W.; Amount =(P.W)+(T.D.)

### important fomulea

1. Let rate =R % per annum and Time = T years. Then,
2. P.W. =$$\frac{100 \times \text { Amount }}{100+(R \times T)}$$=$$\frac{100 \times T . D}{R \times T}$$
3. T.D. =$$\frac{(\mathrm{P.W.}) \times \mathrm{R} \mathrm{x} \mathrm{T}}{100}$$=$$\frac{\text { Amount } \mathrm{x} \mathrm{R} \times \mathrm{T}}{100+(\mathrm{R} \times \mathrm{T})}$$
4. Sum=$$\frac{(S.I) \times(T .0 .)}{(S.I .)-(T . D .)}$$
5. (S.I)-(T.D)=S.I  on T.D
6. When the sum is put at compound interest, then P.W. =$$\frac{\text { Amount }}{\left(1+\frac{R}{100}\right)^{\top}}$$