44 months discount, at 8 cent. annum; besides I p cent. for prompt payment. How much ready money must Answ. 4950). I pay? III. When sundry sums are to be paid at different times, find the rebate or present worth of each particular, payment separately, and when so found add them into one sum. Examples. 15. A is indebted to B 4321. payable in 12 months, more 5801. payable in 2 years: now if A has a mind to pay both these sums immediately, rebate being allowed at 8 cent. annum, how much must he pay? -432 comes 400 580500 Answ. £.900 16. What is the rebate of 7561. the one half payable in months, and the other half payable in 6 months after that, at 7 cent. annum? Answ. 371. 10s. 2121d. 17. I have A B's notes riz one for 201. payable in 3 months, and another for 361. payable in 9 months, and having occasion to raise money upon them; I get them discounted at 6 cent. P annum; what money must I receive? Answ. 541. 3s. 123, d. 18. Discounted the following notes at 5 p cent. Pann D's to myself 1501. 10s. payable 37 days hence. A B's to E L 271. 15s. payable in 15 days. BC to T P 181. payable in 15 months. I want to know how much money I must receive? cent. 19. What is the present worth of 2001. at 4 annum, payable, viz. 100l. at 2 months, 501. at 3 months, and 501. at 5 months? Answ. 1981. Os. 6d. 20. What ready money must I pay for 10001. of which 3001. is payable in 1 year; 3001. payable in 2 years; and the rest in 3 years, discounting at 8 cent annum? Answ. 85823791. In like manner we find the present worth of an annuity, rebating at simple interest for any assigned number of years; for suppose it required to find the present worth of an annuity of 1001. it is manifest we must compute the present worth of 1001 due at the first year, also the present worth of 1001, due at the end of the second year, and so on, repeating the operation for every year of the term and it is plain the sum of all these present worths of each year's rent, will be, the present worth of the annuity for the term of years assigned. Examples. 21. How much present money is equivalent to an annoity of 1001. to continue 5 years; rebate being made at 6 cent, annum ? 106 105: 100: 94.33962 pres. worth of 1 year's an. 112: 100: 100: 89.28571 118: 100 :: 100: 84.74576 2 4 5 124 100 :: 100: 80.64516 130: 100 :: 100: 76.92307 Answ. £. 125.93932 or 4251. 18s. 91⁄2 d. 22. What is the present worth of an aunuity of 50%. te continue 6 years, at 5 cent. Anew. 2561 13s. 7d. 23. What is 807. yearly rent to in ready money, at 6' cent? 24. What is a salary of 401. years, worth in ready money, at 4 Answ: 2421. 10s. 9d. annum, simple interest? continue 5 years, worth 25. What is a pension of 301. worth in ready money at 44 cent.? IV. Answ. 3401. 15s. ld. annum, to continue 7 cent? annum, for 5 years, Ans. 1321. 1 Is. 5d. 26. A merchant is indebted 21631. 3s. payable at 12 months; but pays it at the expiration of 5, discounting at the rate of 6 cent. P annum, how much should he pay? Answ 20901. From 12 months, time given, Take 5 Rem. 7 when payment was made, 27. If the aforesaid sum much ought he to pay? was paid in 3 months, how Answ. 20701.. 28. Suppose a bill drawn the 25th of September, 1792, payable 3 months after date, for 540/. 15s. was dise counted on the 18th of October following, at 6 cent. Pannum, what sum was received for it? Answ. 5341. 10s 321d. 29. A merchant owes 1107. payable in 20 months, and 2247. payable in 24 months: the first he pays in 5 months, and the other 1 month after, discount at 8 cent. Pannum: Idemand the sum he paid? Answ. 3001. 30. Dublin, the 27th Sept. 1808, discounted for Leonard Lackcash, Chr Kiteflyer's promissory note at 2 months for 20%. dated the Ist. inst. Edw. Empty's do, dated 17th do. at 3 months for 371. 10s: and Thos. Trusty's bill on Peter Paywell for 50%. at 31 days sight, accepted by said Paywell, the 20th inst. discount 6 cent. ' annum: what must I pay him for said notes and bill? Answ. 1061. 13s. pro Note. Although the foregoing method is the true and per way of casting up discount; yet the usual method in practice is to calculate the interest that would be due upon the sum discounted in the time, which the bill, note or debt hath to run; and deducting the said interest from the sum discounted, to pay the rest as full consideration for the sum discounted this method is readier and easier than the true method before laid down, and in small sums for a short time the difference is inconsiderable, but the difference becomes very considerable, if a large sum be to be discounted; or if the time be long for which the discount is to be allowed. Find the different sums to be paid for 1007. by both methods for 1 month, 1 year, and 10 years, discount being allowed at 6 cent. annum? True method. Common method.. *Note. Three days are allowed beyond the day of date when a bill or note becomes payable, which are called Days of Grace; so these three days must be added, as this bill becomes due according to date 25th December, but aecording to custom on the 28th. From the above it appears that the difference is less than d. for 100%. for 1 month; but becomes more considerable as the time is longer; for by the common method the sum to be paid is 6s. 91⁄2d. too little for a year, and 21. 108. in 10 years. However as the last method is that most generally used in business, it may be proper that the learner be set to work some of the preceding questions thereby. EQUATION OF PAYMENTS Is when several debts are payable at different times, but is mutually agreed between debtor and creditor, that all those several sums be paid at once, and at such a time as that neither party may be wronged thereby; this is called Equating the time of payment, for which this is the Rule, Multiply the sum of each particular payment by is time, then add the products together, and divide the sum by the whole debt, the quotient (by this Rule) is the equated time for the payment of the whole. Examples. 1. Bowes C 6001. whereof 2001. is to be paid at 3 months, 1501. at 4 months, and the rest at 6 months; but they afterwards agreed the whole should be paid at once; required the time? Answ. 4 months, 15 days. 2. A bought of B a quantity of goods which came to 4697. to be paid in the following manner, viz. 2601, at 5 months, and the rest at 7 months, but afterwards they agree to make one payment of the whole; I demand the equated time? Answ. 5 mouths, 26 days. 3. C. owes D a certain sum which is to be discharged in the following manner, viz. at 8 months, at 4 months, and at 9 months. but they afterwards agree to have but one payment of the whole; the equated time is required? Answ. 4 months, 10 days. 4. A debt is to be discharged thus, viz. at present, at 4 months, and at 5 months, and the rest at 6 months: what is the equated time for the whole? Answ. 5 mo. 5. E is indebted to F 2401. which by agreement is to be paid at 5 months hence, but E is willing to pay 40%. down, provided he will give him a longer time for the payment of the remainder, which is agreed on, the time of payment is required? Answ. 6 months. CHAP. VII. EXCHANGE. HE doctrine of Exchange, taken in its full extent, THE would far exceed the bounds of a Chapter in such a Treatise as this; but as far as it is usually considered as a Rule of Arithmetic, it is chiefly comprehended in this Problem, How to Reduct the Money of one Country into that of another, according to any given Rate or Proportion. In most countries they have real and imaginary monies, the real monies are the coins made, or current, in the country. The imaginary are those whereby they keep their accounts and calculate their payments. Par, in exchange, is a supposed equality between the monies of one country and those of another, i. e. when the money received for a * Bill of Exchange is equal in value to the money paid for it, then exchange is said to be at par. The course of exchange is the value which the coin of one country (taken for the standard of exchange) will yield in another. So the par is fixed, being the supposed real value of foreign money in any country; but the course of exchange is variable and fluctuating; being sometime above and sometime below par: For bills of Exchange are a kind of commodity, which rise and fall in price according as there is a greater or less demand for them. SECT. I. Of Exchange between Dublin and London. Dublin and other places of Ireland, exchange immedi ately with London only, and draw their foreign as well as English demands by that channel, so we shall shew first how * A Bill of Exchange is a written order delivered in one place for value received there, for the like value, according to a rate of exchange agreed upon, to be paid in the place on which the bill is drawn. |