OverviewExercise"In the middle of difficulty lies opportunity."
- Albert Einstein
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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. = |
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.) |
4. (S.I.) - (T.D.) = S.I. on T.D.
| 5. When the sum is put at compound interest, then P.W. = |
Amount |
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1 + |
R |
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T |
| 100 |
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