You owe Rs 6,600 in two years. What lump sum clears the debt today? That fair sum is the present worth . The gap is the true discount .
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Q1. The true discount on a bill due 3 years hence at 6% per annum is Rs 990. Find the present worth of the bill.
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Answer: A
The true discount is T.D. = Rs 990. The rate is R = 6% per year. The time is T = 3 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 6 x 3 = 118. So 990 = (x x 18) / 118. Cross-multiplying gives x x 18 = 990 x 118 = 116820. So x = 116820 / 18 = Rs 6490. Present Worth (P.W.) = Amount – T.D. = 6490 – 990 = Rs 5500. Check: P.W. + T.D. = 5500 + 990 = 6490, which matches the Amount.
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Q2. The true discount on a bill due 2 years hence at 5% per annum is Rs 40. Find the amount of the bill.
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Answer: D
The true discount is T.D. = Rs 40. The rate is R = 5% per year. The time is T = 2 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 5 x 2 = 110. So 40 = (x x 10) / 110. Cross-multiplying gives x x 10 = 40 x 110 = 4400. So x = 4400 / 10 = Rs 440. Present Worth (P.W.) = Amount – T.D. = 440 – 40 = Rs 400. Check: P.W. + T.D. = 400 + 40 = 440, which matches the Amount.
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Q3. The true discount on a bill due 4 years hence at 5% per annum is Rs 740. Find the present worth of the bill.
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Answer: B
The true discount is T.D. = Rs 740. The rate is R = 5% per year. The time is T = 4 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 5 x 4 = 120. So 740 = (x x 20) / 120. Cross-multiplying gives x x 20 = 740 x 120 = 88800. So x = 88800 / 20 = Rs 4440. Present Worth (P.W.) = Amount – T.D. = 4440 – 740 = Rs 3700. Check: P.W. + T.D. = 3700 + 740 = 4440, which matches the Amount.
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Q4. The true discount on a bill due 5 years hence at 8% per annum is Rs 3480. Find the amount of the bill.
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Answer: C
The true discount is T.D. = Rs 3480. The rate is R = 8% per year. The time is T = 5 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 8 x 5 = 140. So 3480 = (x x 40) / 140. Cross-multiplying gives x x 40 = 3480 x 140 = 487200. So x = 487200 / 40 = Rs 12180. Present Worth (P.W.) = Amount – T.D. = 12180 – 3480 = Rs 8700. Check: P.W. + T.D. = 8700 + 3480 = 12180, which matches the Amount.
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Q5. The true discount on a bill due 4 years hence at 16% per annum is Rs 5760. Find the present worth of the bill.
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Answer: C
The true discount is T.D. = Rs 5760. The rate is R = 16% per year. The time is T = 4 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 16 x 4 = 164. So 5760 = (x x 64) / 164. Cross-multiplying gives x x 64 = 5760 x 164 = 944640. So x = 944640 / 64 = Rs 14760. Present Worth (P.W.) = Amount – T.D. = 14760 – 5760 = Rs 9000. Check: P.W. + T.D. = 9000 + 5760 = 14760, which matches the Amount.
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Q6. The true discount on a bill due 2 years hence at 20% per annum is Rs 3240. Find the present worth of the bill.
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Answer: B
The true discount is T.D. = Rs 3240. The rate is R = 20% per year. The time is T = 2 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 20 x 2 = 140. So 3240 = (x x 40) / 140. Cross-multiplying gives x x 40 = 3240 x 140 = 453600. So x = 453600 / 40 = Rs 11340. Present Worth (P.W.) = Amount – T.D. = 11340 – 3240 = Rs 8100. Check: P.W. + T.D. = 8100 + 3240 = 11340, which matches the Amount.
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Q7. The true discount on a bill due 3 years hence at 8% per annum is Rs 408. Find the amount of the bill.
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Answer: D
The true discount is T.D. = Rs 408. The rate is R = 8% per year. The time is T = 3 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 8 x 3 = 124. So 408 = (x x 24) / 124. Cross-multiplying gives x x 24 = 408 x 124 = 50592. So x = 50592 / 24 = Rs 2108. Present Worth (P.W.) = Amount – T.D. = 2108 – 408 = Rs 1700. Check: P.W. + T.D. = 1700 + 408 = 2108, which matches the Amount.
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Q8. The true discount on a bill due 5 years hence at 20% per annum is Rs 6050. Find the present worth of the bill.
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Answer: A
The true discount is T.D. = Rs 6050. The rate is R = 20% per year. The time is T = 5 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 20 x 5 = 200. So 6050 = (x x 100) / 200. Cross-multiplying gives x x 100 = 6050 x 200 = 1210000. So x = 1210000 / 100 = Rs 12100. Present Worth (P.W.) = Amount – T.D. = 12100 – 6050 = Rs 6050. Check: P.W. + T.D. = 6050 + 6050 = 12100, which matches the Amount.
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Q9. The true discount on a bill due 4 years hence at 8% per annum is Rs 848. Find the amount of the bill.
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Answer: D
The true discount is T.D. = Rs 848. The rate is R = 8% per year. The time is T = 4 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 8 x 4 = 132. So 848 = (x x 32) / 132. Cross-multiplying gives x x 32 = 848 x 132 = 111936. So x = 111936 / 32 = Rs 3498. Present Worth (P.W.) = Amount – T.D. = 3498 – 848 = Rs 2650. Check: P.W. + T.D. = 2650 + 848 = 3498, which matches the Amount.
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Q10. The true discount on a bill due 2 years hence at 20% per annum is Rs 2520. Find the present worth of the bill.
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Answer: C
The true discount is T.D. = Rs 2520. The rate is R = 20% per year. The time is T = 2 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 20 x 2 = 140. So 2520 = (x x 40) / 140. Cross-multiplying gives x x 40 = 2520 x 140 = 352800. So x = 352800 / 40 = Rs 8820. Present Worth (P.W.) = Amount – T.D. = 8820 – 2520 = Rs 6300. Check: P.W. + T.D. = 6300 + 2520 = 8820, which matches the Amount.
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Q11. The true discount on a bill due 5 years hence at 16% per annum is Rs 4480. Find the amount of the bill.
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Answer: B
The true discount is T.D. = Rs 4480. The rate is R = 16% per year. The time is T = 5 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 16 x 5 = 180. So 4480 = (x x 80) / 180. Cross-multiplying gives x x 80 = 4480 x 180 = 806400. So x = 806400 / 80 = Rs 10080. Present Worth (P.W.) = Amount – T.D. = 10080 – 4480 = Rs 5600. Check: P.W. + T.D. = 5600 + 4480 = 10080, which matches the Amount.
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Q12. The true discount on a bill due 5 years hence at 12% per annum is Rs 3270. Find the amount of the bill.
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Answer: A
The true discount is T.D. = Rs 3270. The rate is R = 12% per year. The time is T = 5 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 12 x 5 = 160. So 3270 = (x x 60) / 160. Cross-multiplying gives x x 60 = 3270 x 160 = 523200. So x = 523200 / 60 = Rs 8720. Present Worth (P.W.) = Amount – T.D. = 8720 – 3270 = Rs 5450. Check: P.W. + T.D. = 5450 + 3270 = 8720, which matches the Amount.
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Q13. The true discount on a bill due 4 years hence at 20% per annum is Rs 5400. Find the present worth of the bill.
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Answer: D
The true discount is T.D. = Rs 5400. The rate is R = 20% per year. The time is T = 4 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 20 x 4 = 180. So 5400 = (x x 80) / 180. Cross-multiplying gives x x 80 = 5400 x 180 = 972000. So x = 972000 / 80 = Rs 12150. Present Worth (P.W.) = Amount – T.D. = 12150 – 5400 = Rs 6750. Check: P.W. + T.D. = 6750 + 5400 = 12150, which matches the Amount.
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Q14. The true discount on a bill due 3 years hence at 12% per annum is Rs 1890. Find the present worth of the bill.
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Answer: A
The true discount is T.D. = Rs 1890. The rate is R = 12% per year. The time is T = 3 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 12 x 3 = 136. So 1890 = (x x 36) / 136. Cross-multiplying gives x x 36 = 1890 x 136 = 257040. So x = 257040 / 36 = Rs 7140. Present Worth (P.W.) = Amount – T.D. = 7140 – 1890 = Rs 5250. Check: P.W. + T.D. = 5250 + 1890 = 7140, which matches the Amount.
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Q15. Find the present worth of Rs 4050 due 1 year hence, at 8% per annum simple interest.
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Answer: B
The amount due after 1 year is Rs 4050. The rate is R = 8% per year. The time is T = 1 year. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 4050 = 405000. The denominator is 100 + 8 x 1 = 108. So P.W. = 405000 / 108 = Rs 3750. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 4050 – 3750 = Rs 300. Check: P.W. + T.D. = 3750 + 300 = 4050, which matches the Amount.
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Q16. Find the true discount on Rs 16100 due 4 years hence, at 25% per annum simple interest.
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Answer: C
The amount due after 4 years is Rs 16100. The rate is R = 25% per year. The time is T = 4 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 16100 = 1610000. The denominator is 100 + 25 x 4 = 200. So P.W. = 1610000 / 200 = Rs 8050. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 16100 – 8050 = Rs 8050. Check: P.W. + T.D. = 8050 + 8050 = 16100, which matches the Amount.
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Q17. Find the true discount on Rs 11180 due 5 years hence, at 6% per annum simple interest.
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Answer: A
The amount due after 5 years is Rs 11180. The rate is R = 6% per year. The time is T = 5 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 11180 = 1118000. The denominator is 100 + 6 x 5 = 130. So P.W. = 1118000 / 130 = Rs 8600. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 11180 – 8600 = Rs 2580. Check: P.W. + T.D. = 8600 + 2580 = 11180, which matches the Amount.
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Q18. Find the true discount on Rs 1890 due 2 years hence, at 4% per annum simple interest.
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Answer: B
The amount due after 2 years is Rs 1890. The rate is R = 4% per year. The time is T = 2 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 1890 = 189000. The denominator is 100 + 4 x 2 = 108. So P.W. = 189000 / 108 = Rs 1750. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 1890 – 1750 = Rs 140. Check: P.W. + T.D. = 1750 + 140 = 1890, which matches the Amount.
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Q19. Find the true discount on Rs 12606 due 4 years hence, at 8% per annum simple interest.
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Answer: C
The amount due after 4 years is Rs 12606. The rate is R = 8% per year. The time is T = 4 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 12606 = 1260600. The denominator is 100 + 8 x 4 = 132. So P.W. = 1260600 / 132 = Rs 9550. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 12606 – 9550 = Rs 3056. Check: P.W. + T.D. = 9550 + 3056 = 12606, which matches the Amount.
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Q20. Find the present worth of Rs 7920 due 2 years hence, at 10% per annum simple interest.
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Answer: D
The amount due after 2 years is Rs 7920. The rate is R = 10% per year. The time is T = 2 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 7920 = 792000. The denominator is 100 + 10 x 2 = 120. So P.W. = 792000 / 120 = Rs 6600. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 7920 – 6600 = Rs 1320. Check: P.W. + T.D. = 6600 + 1320 = 7920, which matches the Amount.
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Q21. Find the present worth of Rs 10010 due 5 years hence, at 6% per annum simple interest.
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Answer: C
The amount due after 5 years is Rs 10010. The rate is R = 6% per year. The time is T = 5 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 10010 = 1001000. The denominator is 100 + 6 x 5 = 130. So P.W. = 1001000 / 130 = Rs 7700. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 10010 – 7700 = Rs 2310. Check: P.W. + T.D. = 7700 + 2310 = 10010, which matches the Amount.
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Q22. Find the true discount on Rs 11960 due 2 years hence, at 15% per annum simple interest.
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Answer: B
The amount due after 2 years is Rs 11960. The rate is R = 15% per year. The time is T = 2 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 11960 = 1196000. The denominator is 100 + 15 x 2 = 130. So P.W. = 1196000 / 130 = Rs 9200. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 11960 – 9200 = Rs 2760. Check: P.W. + T.D. = 9200 + 2760 = 11960, which matches the Amount.
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Q23. Find the true discount on Rs 7140 due 2 years hence, at 10% per annum simple interest.
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Answer: D
The amount due after 2 years is Rs 7140. The rate is R = 10% per year. The time is T = 2 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 7140 = 714000. The denominator is 100 + 10 x 2 = 120. So P.W. = 714000 / 120 = Rs 5950. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 7140 – 5950 = Rs 1190. Check: P.W. + T.D. = 5950 + 1190 = 7140, which matches the Amount.
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Q24. Find the present worth of Rs 5605 due 3 years hence, at 6% per annum simple interest.
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Answer: A
The amount due after 3 years is Rs 5605. The rate is R = 6% per year. The time is T = 3 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 5605 = 560500. The denominator is 100 + 6 x 3 = 118. So P.W. = 560500 / 118 = Rs 4750. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 5605 – 4750 = Rs 855. Check: P.W. + T.D. = 4750 + 855 = 5605, which matches the Amount.
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Q25. Find the true discount on Rs 1440 due 5 years hence, at 12% per annum simple interest.
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Answer: D
The amount due after 5 years is Rs 1440. The rate is R = 12% per year. The time is T = 5 years. Present Worth (P.W.) is the sum that, invested now at this rate, would grow to the Amount by the due date. The formula is P.W. = (100 x Amount) / (100 + R x T). The numerator is 100 x 1440 = 144000. The denominator is 100 + 12 x 5 = 160. So P.W. = 144000 / 160 = Rs 900. True Discount (T.D.) is the reduction for paying early: T.D. = Amount – P.W. T.D. = 1440 – 900 = Rs 540. Check: P.W. + T.D. = 900 + 540 = 1440, which matches the Amount.
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