(2) At what rate must I invest £60 to obtain the yearly sum of £3 12s.? Here £60 has to produce £3 12s. per annum. The question therefore is, what is the rate per cent.? that is, how much would £100 produce? £ 60 By Rule of Three. The rate is therefore 6 per cent. (3) A man invests £1585 10s. in 3 per cents. at 941, brokerage is charged at the rate of per cent. ; what income does he derive? Every £100 Stock produces £3 per annum. costs £(94 + 1) = £94%. :. £94 produces £3 per annum. The question now is, how much per annum will £1585 produce? (4) What rate of interest arises from money invested in the 7 per cents. at £175? Here every £100 Stock produces £7 per annum. .. £175 produces £7 per annum. We now have to find the rate per cent.; that is, how much £100 produces. Then, by Rule of Three, That is, the rate of interest is 4 per cent. on the money invested. (5) In which Stock is it more advantageous to invest; in the 34 per cents. at 91%, or in the 3 per cents. at 93g? How much Stock may be purchased by investing £1000 in each ? In the 3 per cents. £91 produces an income of £31. Now, we must find how much £91 produces in the 3 per cents. .. In the 3 per cents. £91 produces an income of £3894. Comparing the two incomes produced by the same sum of money in the two different Stocks, we find that the income produced in the 3 per cents. is the greater; that is, it is the more advantageous to invest in. Again, in the 3 per cents., since 91 purchases £100 Stock, Then, by Rule of Three, And, in the 3 per cents., since £93 purchases £100 Stock, £ 939 : 1000 :: 100 : 1068,0 That is, £1000 purchases £1068,88 Stock at 3 per cent. 749 (6) A person invests £4800 in the 4 per cents. at 80, and at the end of each year invests the dividend which becomes due in the same Stock at the same price. Find his dividend at the end of the third year. Since £100 Stock costs £80, .. Dividend at end of Ist year = interest on £6000 at 4 per And £240 will purchase £300 Stock at £80. .. Total amount of Stock in 2nd year .. Dividend at end of 2nd year = = £6300. interest on £6300 at 4 per And £252 will purchase £315 Stock at 80. .. Total amount of Stock in 3rd year = £6300 + £315=£6615. .. Dividend at end of 3rd year cent. for one year = £264 125. = interest on £6615 at 4 per (7) A person invests £1037 10s. in the 3 per cents. at 83, and when the funds have risen 1 per cent. he transfers his capital to the 4 per cents. at 96; find the alteration in his income. £83 will purchase £100 Stock. .. £1037 10s. will purchase £1250 Stock. Income from this Stock, at 3 per cent. = He sells each £100 Stock for £84. £37 10s. .. He sells £1250 Stock for £1050. .. Income from this Stock = £43 15s. Subtract Ist income £37 10s. .. Alteration in his income = £65s. increase. Exercise 6. (Note.--The following examples are all taken from Government Examination Papers.) (1) When the 3 per cents. are at 913, what amount of Stock can I buy for £1835? and what rate of interest shall I get for my capital? (2) What must be given for £5050 Stock in the 3 per cents. at 85 per cent.? (3) How much money must a person invest in the 3 per cents. when the price of Stock is 90% per cent., in order that his halfyearly income may equal £50? (4) If I invest £1200 in the 3 per cents. at 72, what is my income? and how much per cent. do I get for my money? (5) What is the price of the 3 per cents. when £3930 invested in them produces £130 per annum ? (6) How much Stock can be purchased for £3116 55. in the 34 per cents. standing at 103? What income will it yield? (7) What percentage and what amount of interest will an investor receive who puts his capital, £19,500, into the 3 per cents., standing at £89%, commission being per cent. ? (8) Find the yearly income from investing £3960 in Railway Stock standing at 103, and paying 54 per cent. (brokerage being per cent.) (9) Find the yearly income arising from £6040 in the 3 per cent. Consols selling at 948 per cent. (10) Find the selling price of the 3 per cent. Consols when an outlay of £3020 produces a yearly income of £96. (11) I sold out of the 3 per cents. at 96, and invested the sum accruing in railway 5 per cent. Stock, thereby increasing my income 50 per cent. What was the price of the Railway Stock? (12) What amount of 7 per cent. Stock at 106 will £585 15s. purchase, and what will be the interest upon it? (13) How much must I invest in the 3 per cents. at 911, in order to have an income of £150 10s. a year? (14) A capitalist invests £5187 10s. in the 3 per cents. at 83; he transfers of this sum to the 4 per cents. at 96. Find the alteration in his income. (15) What is the yearly interest on £27,225 bought into the 34 per cents. at 97? (16) Which is the better Stock for investment, the 3 per cents. at 92, or the 3 per cents. at par? (17) If a person invest in 4 per cent. Stock at 77, at what rate per cent. will he receive interest for his money? (18) What must be the market value of 3 per cent. Stock, so that, after deducting an income-tax of 10d. in the £, it may yield 3 per cent. interest? (19) What sum of money must be invested in the 5 per cent. Stock at 83 to enable the possessor to realize an income of £64 3s. 4d. per calendar month? (20) What price are the 3 per cents. at when a man buys Stock producing £17 10s. a year for £401 13s. 4d.? (21) The 3 per cents. standing at 98, what sum must be invested in them to produce an annual income equal to the whole interest on £500 for 14 years at 2 per cent.? (22) If I invest £650 in the 3 per cents. at 92}, and sell out when they have fallen to 91, what shall I lose by the transaction? (Note.-On £92 he loses ; it is required to find how much he loses on £650.) (23) A speculator buys shares when they are at 19, £15 having been paid up, and sells them again at £32 95. when £25 has been paid up. How much per cent. does he gain or lose? (24) A speculator invests £4800 in 4 per cents. at 80, and at the end of each year invests the dividend due in the same Stock. If the funds remain at 80 for 3 years, find his dividend at the end of the third year. PROFIT AND LOSS. This subject includes questions which refer to the gain or loss made by merchants in commercial transactions, whether calculated in money or in rate per cent. Questions of this kind are solved by the ordinary rules of arithmetic. They are based on the consideration of two things, (a) the Cost price, (b) the Selling price. (1) Bought 76 yards of muslin at 11s. 8d. per yard; sold it at 14s. 2d. per yard. What was the gain upon the whole? 14s. 2d. IIS. 8d. = 2s. 6d. .. Whole gain =2s. 6d. × 76 (2) If tea be bought at £1 per lb., and sold at ‘I of a guinea, what is the gain per cent. ? We have now the gain on 25., and it is required to find the gain per cent.; that is, the gain on £100. |