A SIMPLE RULE FOR CALCULATING THE TRUE DISCOUNT, and present worth of a sum of money, may be derived from the principle stated above, as follows:

RULE.-Multiply 100 by 365, if for days, or by 12, if for months, as the case may be. Then multiply the rate by the given days, or months; and add both the products together.

To find the PRESENT WORTH, say-As the sum of the products is to the first product, so is the debt to its present worth; then work out the question by Simple Proportion.

To find the DISCOUNT, say-As the sum of the products is to the second product, so is the debt to the discount.

The Example in the previous page will stand as under.

100 x 365 = 36500

4 x 210 = 840

Sum

Again,

Present worth..

37340 36500 :: £3725 11 9: £3641 15 61 185.

Here 365 210 :: £4:

.. £(100 + + x210):

4
365

365

= Interest of £100 for 210 days;

: £100 :: £3725, 11s. 9d.: present worth.

If the first and second terms be multiplied by 365, which does not alter the ratio, it becomes 100 × 365 + 4 × 210: 365 × 100 :: £3725, 11s. 9d.: present worth; but the first term is 100 × 365 +4 x 210; that is, 100 multiplied by the number of days in a year the rate per cent. multiplied by the number of days for which the discount is to be given; and the second term is 100, multiplied by the number of days in a year. To find the discount, the second term of the proportion is 4 × 210, and the other terms the same as before.

THE REASON OF THE RULE is obvious from the above remarks.

Exercises.

4. What is the present worth of £456, 13s., due 146 days hence, and the true discount on the debt? Ans. £447, 13s. 11ąd. present worth; £8, 19s. 02d. 1 discount.

5. What sum of money will now pay a debt of £1000, due 2 years hence, interest at 3 per cent., and what is the true discount on the £1000? Ans. £934, 11s. 72d. present worth; £65, 8s. 4 d. discount.

6. What is the present value of £461, 12s. 3d., due 11 months hence, interest at 43 per cent., and the true discount on the debt? Ans. £442, 7s. 04d. 3483 present value; £19, 5s. 2 d. 1833 discount.

7. I owe £738 in 23 days, £276 in 101 days, and £372 in 219 days. How much money will discharge these debts at present, interest being allowed at the rate of 4 per cent.?

Ans. £1372, 8s. 10d. 118

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.

RULE. 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; and when the rate is 1, 2, &c., these fractions of a pound are meant ; when the rate is expressed in shillings and pence, take proportionate aliquot parts; thus, for 15s. take of £1.

THE REASON OF THE RULE will be obvious by stating the accounts, as in Simple Proportion.

Example 1.-What is the commission on £735, 15s. 8d., at 3} per cent.?

£ 8. d. 735 15 8

3

2207 7 0 367 17 10 1,00)25,75 4 10 20

15,04
12

0,58

4

2,32

100

= &

Pupil. In this example, I multiply £735, 158. 8d. by 3; the product is £2575, 48. 10d. This product I now divide by 100, and the quotient, £25, 158. Od., is the commission required.

The answer may be readily found within a farthing, by annexing half the number of shillings to the pounds of the product, and pointing off three right-hand figures as decimals, then valuing the decimal. Thus, in the present example, half the number of shillings in the product is 2; this 2 annexed to the pounds, £2575, gives £25752. Pointing off the three right-hand figures, we have £25.752, which is equal to £25, 158. Od.

Example 2.-What is the brokerage on £697, 13s. 9d. at 4s. 8d. per cent.?

Exercises.-What is the commission on the following sums?

1. £325, 19s. 11d. at 5 per cent.
2. £695, 10s. 114d. at 3 per cent.
3. £384, 178. 9d. at 2 per cent.

4. £1234, 15s. 6d. at 44 per cent. .
5. £479, 1s. 8d. at 33 per cent.
6. £673, 2s. 6d. at 54 per cent.
7. £7854, 148. 3d. at 43 per cent.
8. £572, 4s. 64d. at 121 per cent.

Ans.

£16 5 113

"

20 17 32

7 13 114

"

55 11 31

"

17 19 3

"

35 6 94

"

382 18 49

"

What is the brokerage on the following sums?

9. £439, 12s. 6d. at 3s. 4d. per cent. 10. £975, 10s. 3d. at 5s. 6d. per cent. 11. £1025, 15s. 4d. at per cent. 12. £731, 17s. 94d. at 4 per cent. 13. £456, 7s. 8d. at 7s. 6d. per cent. 14. £840, 98. at 3 per cent.

15. £5239, 1s. 4d. at 2s. 9d. per cent. 16. If a broker sells goods to the amount of £725, 14s., what is his allowance at per cent.? Ans. £2, 14s. 52d. 13.

17. A broker procures sales for his employer to the amount of £1565, required his allowance at per cent. Ans. £7, 16s. 6d.

18. An agent annually disposes of woollen stuffs to the amount of £820, 14s. 6d. ; of cotton to the amount of £327, 15s. 4d.; of linen to the amount of £120, 198.; of silk to the amount of £316, 148. 9d.; and of other manufactures to the amount of £6432, 11s. 5d.; what is his annual income, supposing his commission to be at the rate of 4 per cent.? Ans. £320, 158.

19. An agent is allowed 5 per cent. for selling goods and guaranteeing the debts to his employers. His sales in a year amount to £23514, 16s. 9d., his losses to £600, 11s. 3d., and the necessary charges attending the business are £117, 4s. 4d.; what is his net annual income? Ans. £575, 10s. 8d. 21. When an agent guarantees the debts to his employer, his commission is called a Del-credere commission.

20. An agent shipped for his employers goods to the value of £561, 4s. 10d.; the charges of package, porterage, &c., amounted to £3, 15s. 6d. ; the shipping charges to £5, 10s. 8d. He is allowed 21 per cent. on the sum laid out; required the amount of the invoice, Ans. £584, 16s. 3 d. 1.

See Invoice, pp. 74 and 184.

21. An agent sent his employer in Jamaica an account of the sales of 50 hhd. of sugar, amounting to £2750, 18s. 9d.; commission at 2 per cent., and brokerage per cent.; duty, freight, and other charges, £935, 7s. 6d. ; what was the net proceeds due to his employer? Ans. £1733, 0s. 84d.

See Account Sales, p. 185.

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.

In the following exercises, the stamp-duty on the policy, and the commission on the amount insured, are added to the premium, to give the whole expense of the insurance.

When the amount insured is not an exact number of £100, the policy-duty is calculated on the number of £100 next greater than the amount insured; thus, if the amount insured is £350, the policy-duty is calculated on £400.

Example. What is the expense of insuring a cargo valued at £754, 14s. 7d., the premium being 3 guineas per cent., policy-duty 5s. per cent., and commission per cent.?

Prem. on £754, 14s. 7d. at 3 guin. per cent. = 23 15 5 nearly.

Required the premium on the following sums.

1. £780 at 2 guineas per cent. 2. £1965 at 3 guineas per cent. 3. £873 at 4 guineas per cent. 4. £695 at 5 guineas per cent.

Ans. £20, 9s. 6d. Ans. £67, 1s. 14d. §. Ans. £43, 10s. 94d. .

5. Find the expense of insuring household amount of £650, the premium being 1s. 6d. per duty 3s. per cent.

Ans. £36, 9s. 9d.

property to the cent., and policyAns. £1, 10s. 9d.

6. What is the expense of insuring £780 on goods from Leith to London at 14 guineas per cent., policy-duty 2s. 6d. per cent., and commission per cent.? Ans. £17, 3s. 84d. §.

7. What is the whole expense of insuring £1821 on goods from Oporto to Leith, premium 51⁄2 guineas per cent., policy-duty 5s. per cent., and commission per cent.? Ans. £119, Os. 44d. 25.

8. What is the expense of insuring £2670 on goods from London to Jamaica at 64 guineas per cent., policy-duty 5s. 3d. per cent., and commission per cent.? Ans. £195, 13s. 1d.

9. What is the expense of insuring £3587 on a brewery at 2s. 6d. per cent., and policy-duty 3s. per cent.? Ans. £9, 17s. 8ęd. §.