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 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 FORMULAE

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

1 . P.W  = \( \frac { 100 \times Amount } { 100(R \times T)} \)=  \(\frac { 100\times T.D } { R \times T } \)

2 . T .D = \(\frac { (P.W)\times R\times T } { 100 } \)= \( \frac { Amount \times R\times T} { 100(R \times T)} \)

3.  Sum = \( \frac {( S.I)\times(T.D) } { ( S.I)-(T.D) } \)

4.  (S.I.) - (T.D.) = S.I. on T.D.

5. When the sum is put at compound interest, then P.W. = \(\frac { Amount } { [ 1+ R/100]^T} \)