# Important Formulas - True Discount - Tricks & Shortcuts

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 P.W.; Amount = (P.W.) + (T.D.)**
Interest is
reckoned on P.W. and true discount is reckoned on the amount.

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

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

1)

2)

3)

4)

5)

**P.W. = (100 x Amount) /(100 + (R x T)) = (100 x T.D) / (R x T)**

2)

**T.D. = ((P.W.) x R x T) / 100 = (Amount x R x T) / (100 + (R x T))**3)

**Sum = ((S.I.) * (T.D.)) / ((S.I.) - (T.D.))**4)

**(S.I.) - (T.D.) = S.I. on T.D.**5)

**When the sum is put at compound interest, then P.W. = Amount /(1+(R/100))**^{T}
Important Formulas - True Discount - Tricks & Shortcuts
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