# Number System - Discounts

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 R. 156 in 4 years. So, the payment of Rs. 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 Present Worth; Amount = Present Worth + True Discount

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,

```P.W. =	(100 x Amount) / (100 + (R x T))
= (100 x T.D.)/ (R x T)
```
```T.D. = (P.W. x R x T) / 100
= (Amount x R x T) / (100 + (R x T))
```
```Sum = (S.I. x T.D.) / (S.I. - T.D.)
```
```S.I. - T.D.  = S.I. on T.D.
```
```When the sum is put at compound interest, then
P.W. = Amount/ (1+R/100)T
```

## Solved Examples

Solved Examples
aptitude_discounts.htm 