4 In 75 tales of China, how much United States money? Ans. D111.00 Ans. D121.87.5 5. In 25 sovereigns, how many dollars? Ans. D94.00 DISCOUNT. DISCOUNT is an allowance made for the payment of any sum of money before it becomes due, and is the difference between that sum, due some time hence, and its present worth. The present worth of any sum or debt not yet due, is so much as would, if put to interest, produce a sum equal to the discount; or the interest of the present worth and interest of the discount for the given time and rate per cent. shall be equal to the interest of the given sum, or debt, for the same time and rate per cent. Thus the present worth and discount of D100 for 1 year at 6 per cent.; the present worth is D94.34, which subtract from D100, gives D5.66 discount, and the interest of D94.34 is D5.66, so that neither party is wronged, provided they are both agreed; but in no case should the interest be allowed on the given sum as discount, because the interest would be D6.00, which is 34 cents too much. Again, if I give my note for D106, payable one year hence, the present value of the note will be less than D106 by the interest on its present value for one year; that is, its present value will be D100. The amount named in a note is called the face of the note; thus D106 is the face of the above note; the discount is the difference between the face of a note and its present value-that is, D6 is the discount on the above note.. EXTRACT. That an allowance ought to be made for paying money before it becomes due, which is supposed to bear no interest till after it is due, is very just and reasonable; but if I pay it before it is due, I give that benefit to another. Therefore, we have only to inquire what discount ought to be allowed. Many suppose that by not paying till it becomes due they may employ it at interest; therefore, by paying it before due, they shall lose that interest and for that reason all such interest ought to be discounted; but the supposition is false, for they can not be said to lose that interest till the time arrives when the debt becomes due; in other words, they can not lose what they do not possess, whereas we are to consider what would be lost at present by paying the debt before it becomes due; this can in point of equity be no other .han such a sum, which being put out at interest till the debt shall become due, would amount to the interest of the debt for the same time, as before observed. The truth of the rule for working is evident from the nature of simple interest; for since the debt, or face of the note, may be considered as the amount of some principal (called here presFent worth), at a certain rate per cent., and for the given time, that amount must be in the same proportion, either to its principal or interest, as the amount of any other sum, at the same rate, and for the same time, to its principal or interest. In what is termed bank discount, the interest is taken for, or called discount. The word is misapplied; the banks loan money and receive interest, not discount. The difference will stand D5.66 to D6.76 on D100 for 1 year, at 6 per cent. (See Bank Interest.) RULE 1. 1. Find the interest of D100 for the time, and at the rate per cent. mentioned in the question; then add this interest to the D100, and this is the first term. 2d. The given sum in the question is the 2d term, and D100 is the 3d term. 3d. Multiply the 2d and 3d terms together, and divide by the first, anl the quotient will be the present worth. 4th. When the discount is required, subtract the present worth thus found, from the given sum, and the remainder is the discount. QUESTIONS. 1. Required the present worth and discount of D500, due } year hence, at 6 per cent. ? D100 Thus RULE II. Assume any principal at pleasure, and find the amount for the time and rate per cent. Then, as the amount found is to the amount or debt given, so is the principal assumed to the required principal, or present worth. 2. Suppose a debt of D810, were to be paid three months hence, allowing 5 per cent., what is its worth in cash ? 3. Purchased goods to the amount of D750, on a credit of 9 months, at 5 per cent., but wishing to make immediate payment, it is required to know what sum in ready money would discharge the debt. Ans. D722.89.1+ 4. What is the discount on D280, due in 6 months, at 7 per cent. ? 5. What is the present worth of D840, months, at 6 per cent. ? 6. What is the present worth of D954, due per cent.? Ans. D9.46.9+ due in 1 year, 6 Ans. D770.64.2. in 3 years, at 4.5 Ans. D840.52.8. 7. If you purchased goods to the amount of D796.49, on a credit of 4 months, at 3 per cent., what sum in ready money would discharge the debt? Ans. D788.60.3. 8. What difference is there between the interest of D1200 at 5 per cent. per annum, for 12 years, and the discount of the same sum at the same rate and time? Ans. D270. 9. What sum in ready money must be received for a bill of 900D. due 73 days hence, discount at 6 per cent. per annum? Ans. D889.32.8. 10. What sum will discharge a debt of D615.75, due in 7 months at 4 per cent. per annum? Ans. D600. 11. B. has D2000 due him from A., of which D500 are payable in 6 months, D800 in 1 year, and the remainder at the expiration of 3 years at 6 per cent. ; but if A. should make present payment, how much would he have to pay? Ans. D1833.37.4+ Note.-When payments are to be made at different times, find the present value of the several sums separately, and their sum will be the present value of the note or debt. 12. What sum will discharge a debt of D1000, whereof D600 is payable in one year, and the remainder in 6 months, at 4 per cent.? Ans. D969.08. 13. What is the present worth of D600 due in 5 years at 7 per cent.? Ans. D444.44.4+ 14. What is the difference between the interest and discount of D1000 for 1 year at 6 per cent.? Ans. D3.39.6+ 15. What is the present value of a note for D3500, on which D300 are to be paid in 6 months, D900 in 1 year, D1300 in 18 months, and the remainder at the expiration of 2 years, the rate of interest being at 6 per cent. per annum? Ans. D3225.83+ 16. What is the present value of D2880, one half payable in 3 months, one third in 6 months, and the remainder in 9 months, at 6 per cent. per annum? Ans. D2810.08+ 17. Bought goods to the amount of D1854 for which I gave my note for 8 months at 6 per cent. ; but being desirous of taking it up at the expiration of 2 months, what sum does justice require me to pay? Ans. D1800 18. What is the present worth of D515 due 6 months hence? D500-due 1 year hence? D485.84.9-due 15 months hence? D479.06.9-due 20 months hence? D468.18.1-due 4 years hence? D415.32.2-at 6 per cent. ? Ans. D2348.42.1+ 19. What is the present worth of D1350, due 5 years 10 months hence, at 6 per cent.? Ans. D1000. 20. What is the discount of D460, due 2 years 6 months hence at 6 per cent. ? What is discount? REVIEW. Ans. D60. What is present worth? How will you first proceed to find the present worth? After having found the interest of D100 at the given time and rate per cent. what is next to be done? After having added the interest so found to D100, by what rule do you work to find the discount? Repeat the rule. Is it correct to take the interest for the discount? What is the difference? What is the face of a note ? When payments are to be made at different times, how do find the present value? 21. What is the difference between the discount of D227.66 for 2 years 3 months and 20 days, and the interest of the same sum for the same time, at 6 per cent. ? Ans. D3.81.2. 22. What is the present worth of D1500 for 90 days at 7 per cent. per annum? Ans. D1474.54+ RULE III. 1. Divide the given sum or debt by the amount of D1 for the given time. 2. The quotient will represent the present worth, which taken from the debt will leave the discount. Thus to find the present worth of D133.20 payable 1 year and 10 months hence, and discount. The amount of D1 for 1 year 10 months, is D1.11; then D133.20 D1.11 D120 present worth; and D133.20-D120-D13.20 discount. EQUATION. EQUATION is a rule used to find the mean or equated time of several payments which are due at different times, so that no loss shall be sustained by either party. RULE I. Multiply each payment by its time, and divide the sum of the several products by the whole debt, and the quotient will be the equated time for the payment of the whole. QUESTIONS. 1. A. owes B. D380 to be paid as follows, namely: D100 in 6 months; D120 in 7 months; and D160 in 10 months; what is the equated time for the payment of the whole debt? 2. I have D200 due me, of which D100 is to be paid in 6 months, and D100 in 12 months, but it is agreed to make one Ans. 9 months. nayment; required the time. |