45. I lent £456 to a friend on March 14, and received as part payment £66 on April 30, £130 on July 11, £120 on August 15, £100 on October 19, and the balance on November 30; how much interest have I to receive, at this last date, at 3 per cent.?

Ans. £6, 13s. 02d. 15.

46. A. received from the bank on March 1, £700, of which he paid £100 on April 1, £100 on May 1, and £100 on the 1st of each succeeding month until the whole amount was paid; how much was the last payment, including the interest at 4 per cent.? Ans. £110, 11s. 32d..

VI. TO CALCULATE THE INTEREST ON ACCOUNTS-CURRENT. AN ACCOUNT-CURRENT is an account in which is drawn out, in Dr. and Cr. (Debtor and Creditor) columns, a statement of the transactions that have taken place between two parties, during a given time.

The term Dr., or debtor, is placed on the left, to shew that the correspondent is debtor for the sums on the left; and the term Cr., or creditor, is placed on the right, to shew that the correspondent is creditor for the sums on the right. The word To, is used to denote Dr.: By, to denote Cr.

Example. Required the interest at 4 per cent. on the following account-current to June 30.

Mr JAMES SIMPSON, London, in Account-current with
ROBERT DUFF, Liverpool.

Dr. 1859.

Cr.

Jan. 18 To Goods,

May 22"

do.

739 15 4

June 16"

Goods,

690 14 4

This account is drawn out by R. Duff, and sent to J. Simpson on June 30. On the left or Dr, side are written all the sums that Simpson owes to Duff; and on the Cr. side the sums that Duff owes to Simpson. Interest at 4 per cent. is then calculated on the account, as below; and as Duff finds that Simpson is due him £3, 8s. 24d, of interest, he enters it on the Dr. side. He next adds the Dr. side, and finds the amount to be £1696, 19s. 93d.; then the Cr. side, which amounts to £1543, 118. 4d. The difference between these, £153, 8s. 5d., is entered on the Cr. side, to balance the account, and then transferred to the Dr. side of a new account, shewing that J. Simpson is owing R. Duff £153, 8s. 53d.

31,117 8

73,000)248,936

Interest, £3 8 21

As the account is supposed to be settled up to June 30, the interest is calculated according to Rule V. page 172, on all the sums on both sides of the account, up to that date: as, for instance, on £360, 14s. 9d. from January 18 to June 30, or for 163 days; and so on. The products of the Dr. side are placed in one column, and of the Cr. side in another; each column is then added, and the smaller of the two sums deducted from the greater; the interest is then calculated on the difference; and the Dr. products in this case being the greater, the interest is entered on the Dr. side of the account-current.

In multiplying the sums by the number of days, the shillings and pence of the products have, for convenience, been left out.

Exercises.

47. Required the interest on the following account to December 31, at 4 per cent. :

Dr. Mr J. MACLAURIN in Account-curt. with W. FERRIE.

Cr.

£340

693

960

123

Nov 11, " do.

Ans. Interest due to Ferrie, £5, 4s. 6d. 172.

48. Jamieson and Son are indebted to Alexander Banks £452 on July 5: they grant him a bill for £165, payable on July 13; and another for £225, payable on August 1; they are due him for goods £347 on August 25, and £127 on September 11; they grant him a bill for £439, due on October 10; and on November

they send goods to the value of £716; on December 17 they receive from him £560. Required the account-current sent to Banks on December 31, allowing interest at 5 per cent. Ans. Jamieson and Son, owe Banks £1, Os. O§d. 4§ for interest; Banks is indebted to them £57, 19s. 114d. 3.

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

0 0

5

105 0
5 5
110 5
5 10

0 1st year.

0 2d year.
6

Ans. £115 15 6 3d

year.

Here we add to the principal, the interest for one year, £5; then to this amount, the interest for the second year, £5, 5s.; and to the last amount, the interest for the third year, £5, 10s. 6d. The total amount at the end of the third year is £115, 15s. 6d.namely, principal, £100; and compound interest, £15, 158. 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. See Compound Interest, page 227, where the subject is treated of at length.

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.

A BILL IS AN AGREEMENT written on stamped paper, in which a debtor agrees to pay to his creditor on a certain day, a specified sum of money which he is owing to him.

The bill may at any period be discounted by a bill-broker or banker. The discounting of a bill consists in giving the money for it, less a certain sum for interest. Thus, if a bill for £100 for three months is discounted at 5 per cent., a charge equal to three months' interest is made by the discounter, and this is his profit for the loan of the money for that period.

The net proceeds, or, present worth of a bill is the net sum that is received for it, after deducting the discount.

According to a practice of old standing, bills are not presentable for payment till the third day after that which is specified for them to fall due. The three days allowed are called the days of grace. Thus, a bill drawn on the 5th of August, at three months, is not legally due till noon of the 8th of November.

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 21 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 5 per cent. on £250,' the meaning is, that discount is to be reckoned at the rate of £5 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.

Example. What is the discount and net 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.?

Bill,

Deduct discount for 72 days,
Net proceeds,

£ s. d. 250 0 0

1 19 6 £248 0 6

Here the bill is payable on December 4, reckoning the three days of grace, 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, 0s. 6d. as the net proceeds.

In discounting bills, any farthings in the answer are considered, by bankers, as a penny; thus, if the discount amounts to £1, 19s. 51d., it is reckoned as £1, 19s. 6d.

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.

Exercises.

1. A bill dated January 1, at 3 months' date, for £739, 16s. 11d., was discounted on February 14. What was the discount and net proceeds? Ans. Discount, £4, 19s. 32d. ; net proceeds, £734, 17s. 72d. 1818.

2. Required the discount and the net 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. 182; net proceeds, £1167, 11s. 64d. 503.

3. 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 net proceeds, allowing interest at 4 per cent., and commission at per cent.? Ans. £2619, Os. 42d. 387. DISCOUNT, AS practically understood, is calculated as above, by deducting the interest for the given time from the principal.

DISCOUNT, IN THE STRICTLY correct SENSE, is ascertained by calculating what is the sum which, with interest for the given time, will amount to the sum on which the true discount is to be taken.

The Interest on the smaller sum thus found, is equivalent to the TRUE DISCOUNT on the given sum; and the smaller sum is called the PRESENT WORTH of the other.

I. TO FIND THE present worth OF A DEBT DUE AT A CERTAIN TIME, THE RATE OF INTEREST BEING GIVEN.

RULE-1. Find, by Simple Proportion, what £100, with interest for the given time and rate, will amount to.

2. Then say, as the AMOUNT of £100, for the given time and rate, is to £100, so is the given debt to the present worth required.

II. TO FIND THE true DISCOUNT ON A DEBT.

RULE-1. Find as before what £100, with interest for the given time and rate, will amount to.

2. Then say, as the AMOUNT of the £100 is to the amount of the debt, so is the interest on £100 to the discount on the debt.

Or, Find the PRESENT WORTH of the debt by Rule I., and the difference between the present worth, and the amount of the debt is the discount.

The Reason of the rule is plain.

Example.-What sum of money will now discharge a debt of £3725, 11s. 9d., due 210 days hence, reckoning interest at 4 per cent.; and what is the true discount on the debt? Answer: Present worth, £3641, 15s. 6d. 1485; Discount, £83, 16s. 24d. 602,

16027.

365 210: £4 £18 the interest of £100 for 210 days. ..£100+£18 £100168 = the amount of £100 for do.

.. £100 100 :: £3725, 11s. 9d. : £3641, 15s. 64d. 138 present worth.

Here, since 4 is the rate per cent., to find the interest for 210 days, we say, as 365 is to 210, so is £4 to £18; hence £100168 is equal to the amount of £100 for 210 days. Again, as £100168 is to 100, so is £3725, 11s. 9d. to the answer. Working out this by Simple Proportion, we obtain £3641, 15s. 6d. 126 for the present worth required.

Again, £100: 3725 11 9:: £168: £83 16 20% discount.

186