IMPORTANT CONCEPTS
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.) = 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 FORMULAE
Let rate = R% per annum and Time = T years. Then,
1. P.W.=[100 x Amount
/100 + (R x T)
=100 x T.D./ RxT
2.
T.D.=[(P.W.) x R x T /100]
= [ Amount x RxT/100 + (R x T)]
3.(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
SOLVED EXAMPLES
Ex. 1. Find the present worth of Rs. 930 due 3 years hence at
8% per annum. Also find the discount.
Sol.
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 Spring '11
 vinh
 Rs., T.D.

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