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42. Find the amount of £325, 16s. 8d. at 45 per cent. simple interest in 3 years.

43. In what time will a sum of money double itself at 31 per cent. per annum, simple interest?

44. A £50 railway share, which cost me £55, pays a yearly dividend of £6; what is my rate of interest?

45. A house which cost £1500 lets for £65 a year; the outgoings for insurance and other expenses amount to 14 per cent. on its cost : what rate of interest does it pay?

46. Find the simple interest on £325, 8s. 4d. for 3 months, at 4 per cent. per annum; and the real discount of £328, 135. 5d., due 3 months hence, at 4 per cent per annum.

47. A loan of £1000 is repaid in instalments as follows:

in 6 months, 1 in 12 months, and the rest at the end of 2 years; what is the total interest which should be paid, at 5 per cent. ?

48. If £100 be placed at interest at 5 per cent., and the interest be added to the principal every 20 years, in how many years will it amount to £1000?

INTEREST (Compound). 1. What will £200 amount to in 3 years at 4 per cent. per annum, compound interest ?

2. Find the compound interest on £254 in 3 years 5 months, at 3 per cent.

3. Find the compound interest of £265 for 3 years, at 5 per cent.

4. Find the compound interest on £820 for 2 years 84 days, at 4 per cent.

5. Find the difference between the simple and compound interest of £150 in 3 years, at 43 per cent.

6. Find the difference between the simple and compound interest on £3600 for 3 years, at 4) per cent.


PRESENT WORTH. 1. What is the present worth of £75 due 15 months hence, at 5 per cent ?

2. What ready money would a person receive for a debt of £184, 155. 9d., if he allowed a discount of 3) per cent. ?

3. Find the present value of £,605, 1os. 6d. due 3 years hence, the rate of interest being £4, 155. per cent. per annum.

4. Find the present worth of £259, 75. due 4 years hence, at 31 per cent simple interest.

5. If the present worth of £838 due at the end of 19 months be £800, find the rate per cent per annum.


COMMISSION, BROKERAGE, etc. 1. If a broker be allowed 38 per cent, what may he demand when he sells goods to the value of £876, 55. rod.?

2. If a collector, who is paid 5 per cent. commission, receives £17, 1os. for his trouble, how much has he collected ?

3. A broker procures an assurance upon property to the amount of £1850; what will he have for his trouble, at 35. od.

per cent. ?

4. A man collecting rents, at a commission of 45 per cent., paid to his employer, after deducting his commission, £1482, 35. 9d. ; what amount of rent did he collect ?

5. A person wished to insure his life, so that at his death his family might receive £360; what had he to pay annually, at £2, 18s. 4d. per cent ?

6. If I pay an annual premium of £45, 155. on a policy of life assurance of £2000, what is the rate per cent at which I assure ?

STOCKS. 1. If a person invest in 4 per cent. stock at 777, at what rate per cent. will he receive interest for his money?

2. What amount of 7 per cent stock, at 1061, will £585, 155. purchase, and what will be the interest upon it?

3. At what rate per cent. will a person receive interest, who invests his capital in the 3 per cents. at 893, commission being $ per cent. ?

4. What amount of Russian 5 per cent. stock, at 941, will £848, 5s. purchase, and what will be the interest on it?

5. A person invests £1037, 1os. in the 3 per cents. at 83, and when the funds have risen i per cent., he transfers his capital to the 4 per cents. at 96 ; find the alteration in his income.


1. If eggs be bought at 5 for three pence, at what price must they be sold to gain 20 per cent. ?

2. I bought coffee at £6, 155. 6d. per cwt ; what should I sell it for to gain 73 per cent. ?

3. A piece of cloth measuring 60 yards was bought for £37, 105. ; how should it be sold per yard to gain 15 per cent. ?

4. By selling cheese at £3, 135. 6d. a cwt., a grocer realized a profit of 221 per cent. ; what did it cost him per cwt. ?

5. If a parcel of goods bought for £18 be sold for £25 four months afterwards, what is the gain per cent per annum?

6. If 24 per cent. be lost by selling bacon at 6d. per lb., what did it cost per cwt. ?

7. If by selling a horse for £96 I lose 20 per cent., what must I have sold it for so as to gain 5 per cent. ?

8. If 4 per cent. be lost by selling linen at 25. 9d. a yard, at what price must it be sold to gain 10 per cent. ?

9. A man bought 2 tons 3 cwt. 3 qrs. of sugar for £120, and paid £2, 1os. for expenses; what must he sell it at per cwt. to clear 50 per cent. ?

10. By selling goods at £2, 125. 3d. I gain 10 per cent. ; what did they cost me?

11. What was the loss per cent. on raisins, which were bought at 335. per cask of 100 lbs., and sold at 3 d. per lb.?

12. If 90,876 articles were purchased at an average price of £5, 125. 6d. per dozen, what would be the total gain by charging afd. additional for each of them, and the gain per cent. ?

13. A grocer buys 5 cwt. of sugar at 5d. per Ib., and 7 cwt. at 6}d. ; he sells 54 cwt of it at 5 d. per lb. : at what rate must he sell the remainder in order to gain 12} per cent. ?

14. By selling a horse for £19 the seller loses 5 per cent. on his outlay; what would have been his loss or gain per cent. if he had sold the horse for £23, 155. ?

15. If by selling tea at 6s. 4d. a Ib. a grocer lose 6 per cent., what did it cost him per lb. ?

16. A house was bought for £64; for what price should it be sold to gain £12, ios. per cent. ?

17. A farmer gave for a horse a bill of £156, due 8 months hence, at 45 per cent., and sold him at once for £180; required his gain per cent.


1. In 1850 the population of the city of London was 129,181 ; in 1861 it was 113,387: find its decrease per cent.

2. The population of a town in 1851 was 15,786, and in 1871, 19,670; find the increase per cent.

3. The percentage of children who are learning to write is 65 in a school of 60 children, and 78 in another school of 70; what is the percentage in the two schools together?

4. The populations of three towns in 1851 were 20325, 42405, and 1423; and in 1861 they had increased respectively 9, 10, and 12 per cent. : find the average population of the three towns in 1861.


1. Divide £345, 1os. among three persons, so that their shares shall be as the numbers 5, 6, and 7.

2. A man owes £110 to A, £97 to B, and £133 to C; his assets are £85: what dividend will each receive ?

3. A twenty-stone bag of flour was divided into an equal number of shares, stone, stone, stone; how many shares were there in all ?

4. Three persons start in business together. A contributes £.84, 1os. ; B contributes £96, 155.; C, £76, 58.; they gain £238, 6s. 8d. : what is each person's share of the profit?

5. Divide 567.58 guineas among 3 men and 4 women, giving each man 175 of a woman's share.

6. Two persons, A and B, enter into partnership. A puts into the business £800, and B £700; how should they divide a year's profit of £450 ?

7. The produce of a farm, viz. 964 bus. 3 pks. I qt. of wheat, is to be divided among three men in proportion to the rent they each pay. The first pays the rent, the second of the remainder, and the third what then remains; how much of the produce will each have ?

8. A field of grass is rented by two persons for £27; the former keeps in it 15 oxen for 10 days, and the latter 21 oxen for 7 days: find the rent paid by each.

9. A bankrupt owes 3 creditors (A, B, C) £290, £556, and £620 respectively; his property is worth £412, 6s. 3d. : what ought each creditor to receive ?

10. Three persons rent a field for £60, 1os. A puts in 5 sheep for 4} months; B, 8 sheep for 5 months; C, 9 sheep for 6 months: what must each pay of the rent ?

11. Three cow-keepers hire a pasture for £35, 75. 6d. for 26 weeks. During the time A puts 7 cows in it for 13 weeks; B, 14 cows for 9 weeks; and C, 3 cows for 22 weeks : how should they divide the rent?

12. Divide £64 among A, B, C, so that A may have three times as much as B, and C may have one-third of what A and B have together.

13. Three men hold a farm in common; one pays £97, another £79, and the third £100 as their shares of the rent. A rate of £34, 1os. is levied on the farm; what is each man's portion ?

14. Two persons joined in business; one of them provided £500 towards stocking their shop, the other £400. At the

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