Suppose a man has to pay Rs. 156 after 4 year 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 Formula:
Let rate = R % per annum and Time = T years. Then
(S.I.) – (T.D.) = S.I. on T.D.
When the sum is put at compound interest, then