TABLE IV, Showing the amount of 1 dollar or 1 pound, from 1 day to 16 years, computed at 365 days to the year. To collect a divisor for days, months, and years: RULE. Take the decimal parts for the different denominations of the given time-the sum more one will be the divisor. EXAMPLE. Required the present worth of $500, due 10 years, 4 months, 14 days hence, discount at 6 per cent. per annum. decimal part by the table for 10 years. add 1. 1.6223 amount of 1. for 10 years, 4 months, and 14 days, and a divisor for any sum at that rate and time. 1 Then 1.6223) 500,000 (308.20. present worth, Answer. 7140 remainder. To prove Discount, cast interest on the present worth, for the the amount should equal the given sum to 308.20 present worth as above. given time and rate be discounted. 8. What is the present worth of $4000, due 75 days hence, discount at 6 per cent. per annum? Ans. $3951.29. 9. What ready money must be paid for a note of $4500, due 60 days hence, discount at 6 per cent. ? Ans. $4456.06. 10. What discount must I deduct from a note of $500, due 45 days hence, at 7 per cent. ? Ans. $4.28. 11. What is the present worth of a bond for $8000, due 4 years, 6 months, 20 days hence, at 6 per cent.? Ans. $6282.95. New-York, 1st Dec. 1802. 12. Discounted the three following notes, viz. George Barnwall's, for $500 due 30th January; Wm. Constable's, - 720 800 15th do. 30th instant: What sum must be deducted for discount, at 6 per cent. ? Ans. $13.96. The difference of Discount and Interest. Interest is almost universally used by merchants for the calculation of discount. For a short time, and small sum, the error is not worth correcting; but when the time is considerable, and the sum large, the error becomes greater than we might at first apprehend. This can be better illustrated by example than argument: EXAMPLE. Required the difference of the discount and interest of $1000 for 1 month, 2 months, 4 months, 8 months, 1 year, 5 years, and 10 years, at 6 per cent. per annum ? 1 month 2 4 8 1 year 5 10 Interest. Thus the seller of a bill or note of $1000, will lose by interest in one month only about 3 cents, for 4 months 22 cents, for 8 months $1.54, for a year $3.39, and for 10 years $225. Present worth of Annuities. The present worth of Annuities is found by dividing each payment by the amount of 1 for the given time, the sum of the different terms found, is the present worth. At first view this appears absurd; because, if interest be calculated on the present worth, the amount will be more than the sum of the annuity; but if interest be counted on the present worth of each payment, for its respective time, the amount will be equal to the annuity for that time. EXAMPLE. What is the present worth of an annuity of $1000 to continue 6 years, discount at 6 per cent. per annum? 1.06-943.40 present worth of 1st yr's. annuity. Some imagine this method of purchasing annuities unjust; that they should be computed at compound interest. Leaving the buyer and seller to settle this matter, we shall give a few examples for the learner's sake, and proceed to factorage and exchange. 2. What is the present worth of an annuity of $500, to continue 5 years, at 5 per cent. per annum ? Ans. $2179.12. 3. What is the present worth of $1200 yearly rent for 8 years, at 6 per cent. per annum? Ans. $ 4. What is the present worth of $600, annuity to continue 7 years, and not to commence till the expiration of 4 years, discount allowed at 7 per cent. per annum? Ans. $2844.06. 5. What is the present worth of £50, annuity to continue 6 Ans. £256 13 7. years, at 5 per cent. per annum? 6. What is £80 annuity worth in ready money, to continue 5 Ans. £340 15 1. years, at 6 per cent. per annum ? 7. What is the present worth of £100 annuity to continue 5 Ans. £425 18 9 years, at 6 per cent. per annum ? Equation of Payments. When several debts are payable at different times, and the Dr. and Cr. mutually agree that all the sums should be paid at once, and at such a time that neither party should sustain loss thereby; this is called equating the time of payment, for which this is the RULE -Multiply each particular payment by its time, add the products, and divide the sum by the whole debt, the quotient is equated time for the payment of the whole. EXAMPLE. 1. A owes B $600; whereof 200 is payable at 3 months, 150 at 4 months, the remainder at 6 months; but they agree that the entire should be paid at once: Required the equated time: Though the above method is in general use, yet it is not strictly true, for we must suppose that in paying a debt before it is due, the discount, not interest, should be lost. But the error is so trifling, and the true method so prolix, that this rule will never go out of use. 2. A bought goods of B, to the amount of $460, to be paid as follows: 260 in 5 months, the remainder in 7 months; but they agree to make one payment of the whole: What is the equated time? Ans. 5 months 262 days. 3. C owes D a certain sum, payable as follows: in 3 mo. in 4 months, and in 9 months; but they agree to make one payment of the entire: Required the equated time: Ans. 4 months 10 days. at 4 4. A debt is to be discharged thus: immediately, months, at 5 months, and the rest at 6 months: At what time may the whole be paid? Ans. 5 months. 5. E is indebted to F £240, which by agreement, is to be paid 5 months hence; but E is willing to pay down £40, provided he has a longer time for the payment of the remainder, which is agreed to: The time of payment is required: Ans. 6 months. Factorage or Commission, Brokerage, &c. A Premium estimated at so much per cent. for the transaction of business by a factor, is called factorage, commission or brokerage. RULE.-Multiply the amount sales, &c. by the rate per cent. divide by 100, the quotient will be the amount, commission, brokerage, &c. Otherwise, Multiply the amount sales by the ratio, (see Tab. 3, simple interest page 117) the product will be the commission, &c. EXAMPLE. 1. What is the commission on an account sales of $6754.50, at 3 per cent. Ans. $236.40. 2. What is the brokerage on $654.40, at per cent.? Ans. $1.63.. 3. What brokerage must be paid on $800.50, at 4 per cent.? Ans. $6.00.+ 4. Sold goods to amount of $345.60: What is my commission on the sales at 34 per cent. ? Ans. $12.96. 6. A factor owes a merchant $1000 neat proceeds, and has orders to lay it out on merchandize, and hold 2 per cent. for his commission and charges: How much must the factor lay out on these terms? Ans. $980.40. 7. A factor owed his employer $456.50 neat proceeds; the merchant thinking it more advantageous to have merchandize for the amount, than to draw, ordered the factor to buy and ship on his account. The factor's invoice is $443.20, the remainder he holds for commission and charges: What rate did he charge? Ans. 3 per cent. |