Exercises.-1. What is the interest on the following account to December 31, at 44 per cent.? Dr. Mr J. MILLER in Account-current with W. FERRIE. Cr. 875 Nov. 29, " Nov. 11, "1 do. Ans. Interest due to W. Ferrie, £5, 4s. 64d. 1727 2. Allan & Son are owing A. Jones £452 on July 5: they grant him a bill for £165, payable on July 13, and another for £225, payable on Aug. 1; they are due him for goods £347 on Aug. 25, and £127 on Sept. Il; they grant him a bill for £439, due on Oct. 10; on Nov. 3, they send goods to the value of £716; on Dec. 17, they receive from him £560. State the account current sent to Jones on Dec. 31, allowing interest at 5 per cent. Ans. Allan & Son owe Jones for interest, £1, Os. 03d. 4; Jones is owing them, £57, 19s. 114d. 23 EXPLANATION OF THE RULES.-The Rules for finding interest are virtually the same as those of Simple and Compound Proportion, according to the nature of the case. · INTEREST for one year is a case of Simple Proportion: for instance, the question, What is the interest on £40 for one year at 5 per cent. ?' may be stated thus: £ £ £ 100 : 40 :: 5 The question, as a case of Simple Proportion, may be expressed in this way-If the interest on £100 is £5, what will be the interest on £40? INTEREST for more than one year, or for days, is a case of Compound Proportion for instance, the question, What is the interest on £250 for 45 days, at 4 per cent. ?' may be stated thus: £ : 100 : 250 :: 3 36,500 11,250 The meaning is :-If the interest of £100 for 365 days is £3, what will be the interest of £250 at the same rate for 45 days? hence it is a question in Compound Proportion. For convenience in working, the first term is doubled, making 73,000; and to put the second term on an equality, it would require to be also doubled, but it is more convenient, and has the same result, to double the third term, and thus multiply by twice the rate per cent. COMPOUND INTEREST is computed by adding to the principal the interest due at any given time, as-at the end of a year; then reckoning interest on this new amount for a similar period, and again adding it as before; and so on. Example.-What will £100 amount to in 3 years, at 5 per ct. compound interest? £100 0 0 500 105 0 0 1st year. 110 5 0 2d year. Ans. £115 15 6 3d year. Here we add to the principal, the interest for one year, £5; then to the amount of the two sums, the interest for the second year, £5, 5s.; and to the last amount, the interest for the third year, £5, 108. 6d. The total amount at the end of the third year is £115, 15s. 6d.namely, principal, £100; and compound interest, £15, 15s. 6d. Compound Interest may be calculated in this way when the time is only two or three years; but for longer dates, this would be a tedious process, and another method is employed, which is treated of in the Advanced work on Arithmetic. DISCOUNT. DISCOUNT is a charge of so much per cent. made by bankers and others, for advancing money upon bills, &c. before they are due. Discount is deducted from the given sum, and is thus the reverse of interest. For an account of Bills, and the discounting of them, see page 134. Discount is also the term applied to the allowance or deduction frequently made at the settlement of accounts. Thus, a person who is owing an account of £100, on settling it, may receive an allowance of 23 per cent.; he would therefore pay only £97, 10s. the remaining £2, 10s. being allowed as discount. When discount at so much per cent. is stated without any time being specified, as, discount 10 per cent. on £250,' the meaning is, that discount is to be reckoned at the rate of £10 for every £100 in the sum. DISCOUNT is calculated in the same way as interest, whether for years, months, or days. When no particular time is specified, it is calculated by Rule I. of Interest. NOTE.-Discount at 10 per cent. is calculated by merely taking th of the given sum-that is, dividing it by 10: thus, discount on £370 at 10 per cent. is £37. Example.-What is the discount and nett proceeds of a bill for £250, dated Aug. 1, due at 4 months after date, which was discounted on Sept. 23, at 4 per cent.? Here the bill is payable on December 4, reckoning the three days of grace (see page 135), that is in 72 days after September 23, the day on which it was discounted. The discount for 72 days is calculated as in Interest, Rule IV. and amounts to £1, 19s. 6d. which being deducted from the bill, leaves £248, Os. 6d. as the nett proceeds. In discounting bills, any farthings in the answer are considered, by bankers, as a penny; thus, if the discount amounts to £3, 2s. 24d. it is reckoned as £3, 2s. 3d. Exercises. What is the discount on the following sums? 1. £124 7 6 at 2 per cent. Ans. £3 2 24 6. A Bill dated Jan. 1, at 3 months' date, for £739, 16s. 11d. was discounted on Feb. 14; what was the discount and nett proceeds? Ans. Discount, £4, 19s. 32d.; Nett proceeds, £734, 17s. 7d. 7. Required the discount and the nett proceeds on the following bills, at 4 per cent. which were discounted on April 4: one for £174, dated February 24, at 4 months; one for £1000, dated March 15, at 2 months, Ans. Discount, £6, 8s. 51d.; Nett proceeds, £1167, 11s. 6d. 8. The following bills were discounted on June 27:-No. 20, for £360, dated April 14, at 5 months; No. 23, for £721, dated May 2, at 3 months; No. 31, for £875, 10s. dated May 15, at 2 months; and No. 32, for £691, 15s., dated June 3, at 4 months. What was the nett proceeds, allowing interest at 4 per cent. and commission at per cent.? Ans. £2619, Os. 42d. COMMISSION AND BROKERAGE. COMMISSION is a charge of so much per cent. made by an agent for buying or selling goods, &c. on account of another. The rate varies from 1 to 10 per cent. BROKERAGE is a similar charge made by persons termed brokers, for assisting others in buying or selling goods, shares, &c. The rate is usually less than 1 per cent. COMMISSION and BROKERAGE are calculated by multiplying the given, sum by the rate per cent. and dividing the product by 100, as in Interest, Rule I. When the rate is 1, 2, 3 per cent. &c. pounds are meant: when the rate is expressed in shillings and pence, take proportionate aliquot parts; thus, for 15s. take 3 of £1, or for 3s. 4d. take of £1. Example.-What is the commission on £700, 10s. at 4 per cent.? INSURANCE. INSURANCE is a contract by which certain persons or insurance offices engage to make good to the party insuring, losses he may sustain of ships or their cargoes at sea, or of houses or goods by fire. The parties who take upon themselves the risk, are called the insurers, or underwriters; and the person protected, the insured; the sum paid to the insurers is called the premium; the stamped paper on which the contract is written, the policy of insurance; and the stamp-duty on the policy, the policy-duty. Besides the premium and duty, there is, in some cases, a commission charged. Sums of money are also insured on persons' lives; an individual contracting to pay a certain premium annually during his life, has a sum insured to be paid to his family at his decease. I. TO FIND THE PREMIUM ON THE SUM INSURED. RULE.-Multiply the given sum by the rate per cent. and divide the product by 100, as in Commission. When the rate is 1, 2, 3 per cent. &c. pounds are meant: when the rate is expressed in shillings and pence, take proportionate aliquot parts; thus, for 15s. take of £1, or for 3s. 4d. take of £1. When the rate is expressed in guineas, calculate as if it were in pounds, and to the result add, for the premium required. Example.-What is the expense of insuring a cargo valued at £648; the premium being 35s. or 12 per cent.? £648 648 = 162 100)1134 (Ans. £11 6 9 Here we multiply £648 by 13, the rate per cent. and then divide the product by 100. Exercises.-What is the premium on the following sums? 1. £376 12 6 at 11 per cent. 2. 742 6 8 " 36s. 3. 780 0 0 2 guineas per cent. 4. 1965 0 0 " 34 " " Ans. £5 12 113 3 "1 13 7 21 "/ 20 9 6 5. Find the expense of insuring household property to the amount of £650, the premium being 1s. 6d. per cent. on the sum insured, and the policy-duty 3s. per cent.* Ans. £1, 9s. 3d. 6. What is the expense of insuring £3587 on a building, the premium being at 2s. 6d. per cent. on the amount insured, and the policy-duty 3s. per cent.? Ans. £9, 17s. 31d.17 *The policy-duty is always charged on even hundreds; thus, if the sum insured is £650, the duty is charged on £700. II. TO FIND HOW MUCH MUST BE INSURED IN ORDER TO COVER A GIVEN SUM, BESIDES PAYING ALL EXPENSES OF PREMIUM, &c. A merchant sometimes insures not only the value of his property, but also the premium, duty, commission, and other charges; so that, in case of loss, he may be entitled to receive from the underwriters, or insurance-office, a sum equal to the value of the property and expenses of insurance. In this case the property is said to be covered. RULE.-Subtract the percentage to be paid for premium, duty, and commission, from £100; then state the case as a question in Simple Proportion, thus: If the remainder-that is, £100 less the expenses-requires to be insured for £100, in order to be covered, what will £2820 require to be insured for ?' Example.-What sum must be insured to cover £3091 in case of loss, the premium being 51s. per cent., policy-duty 4s. per cent., and commission per cent. ? £100, in order to cover £97; the question, therefore, is stated thus: 'If £97 must be insured for £100, what must £3091 be insured for? Exercises. 1. What sum must be insured to cover £750, premium 2 guineas, and commission per cent. ? Ans. £774, 3s. 104d. 2. How much must be insured to cover £675, the premium being 4 guineas, and commission per cent.? Ans. £710, 4s. 112d.78033 3. What sum must be insured to cover £2884, 10s. in case of loss, the premium being 3 guineas per cent., policy-duty 4s. per cent., and commission per cent.? Ans. £3000. 4. How much must be insured to cover £1000, the whole expenses attending the insurance being £8, 7s. 6d. per cent. ? 5. What sum must be insured to expenses attending the insurance being Ans. £1091, 8s. 12d. 71f cover £1250, the whole £5, 15s. per cent.? Ans. £1326, 5s. 24d. 197 |