True Discount - ( 
Arithmetic Aptitude)
IMPORTANT CONCEPTSSuppose 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.IMPORTANT FORMULAELet rate = R% per annum and Time = T years. Then,
4. (S.I.) - (T.D.) = S.I. on T.D.
| 1. P.W. = | 100 x Amount | = | 100 x T.D. |
| 100 + (R x T) | R x T |
| 2. T.D. = | (P.W.) x R x T | = | Amount x R x T |
| 100 | 100 + (R x T) |
| 3. Sum = | (S.I.) x (T.D.) |
| (S.I.) - (T.D.) |
| 5. When the sum is put at compound interest, then P.W. = | Amount | |||||
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