The USE of the TABLE.

First, To know the Number of Days from the Beginning of the Year to any given Day of any Month.

This is obtained by Inspection only; thus, from January the 1st, to August the 8th, is 220 Days; to November the 24th, is 328 Days, &c.

Secondly, To know what is the Number of Days from any given Day of any Month, to the End of the Year. 365 Days,

Suppose August 8th, then from

Subtract the Number answering to August 8,

220

There remains the Number of Days, viz.

.❤

145

Thirdly, To find the Number of Days between the given Day of any Month, and the given Day of any other Month, in the same Year.

For instance, To know how many Days there are between
May the 9th, and November the 5th.
Thus, from the Number answering to Nov. 5,
Subtract that answering to May 9,

The Remainder is the Number of Days sought,

viz.

309 Days,

129

180

Fourthly, To find the Number of Days from any given Day of any Month in one Year, to any given Day of any Month in the next Year.

How many Days is it from October the 12th in one Year, to June the 10th in the next?

Thus, from the Days of a whole Year,

365 Days,

Subtract the Number answering to Oct. 12, viz. 285

Remains the Nunber to the End of the Year,
To which add the Number to June 10,

80

161

The Sum is the Number of Days required, viz.

241

And thus is the Number of Days readily found for

any In

terval of Time given, in the same Year completely; or which

is Part of one, and Part of another Year.

EXAMPLES.

(29) What is the Interest of 200/ for 73 Days, at 31. per Cent per Annum?

(30) What is the Amount of 3407 10s from January 1, 1789, to July 18 following, at 5 per Cent. per Annum? (31) What is the Interest of 500/ from December 4, 1791, to March 10, 1793, at 4 per Cent. per Annum ?

Case 7. When the Amount, Time, and Rate per Cent. are given, to find the Principal.

RULE.

1. Say, As the Amount of 100 at the Rate and Time given is to 1001: so is the Amount given to the Principal required. Or,

2. The Examples in this and the two following Cases may be solved by the Rule in Sect. XV.

EXAMPLES.

(32) What Principal, being put to Interest for 91 Years, at 44 per Cent. per Annum, will Amount to 856/ 10s. ? (33) What Principal, being put out to Interest for 7 Years,

will amount to 6147 3s 11d, at 3 per Cent. per Annum ?

Case 8. When the Principal, Rate per Cent. and the Amount are given, to find the Time.

RULE.

Say, As the Interest of the Principal for a Year: is to 1Year: so is the whole Interest: to the Time required.

EXAMPLES.

(34) In what Time will 600/ amount to 856/ 10s, at 44 per Cent. per Annum?

(35, In what Time will 498/ 6s 8d amount to 614/ 3s 11d, at 3 per Cent. per Annum ?

Case 9. When the Principal, Amount, and Time are given, to find the Rate per Cent.

RULE.

C

1. Say, As the Principal is to the Interest, for the whole Time: so is 1001: to the Interest for the same Time.

2. Divide that Interest by the given Time, and the Quotient will be the Rate per Cent. required.

EXAMPLES.

(36) At what Rate per Cent. per Annum will 600/ amount to 856/ 10s in 94 Years?

per

(37) At what Rate per Cent. Annum will 498/ 6s 8d amount to 614/ 3s 11d in 73 Years?

QUESTIONS for Exercise in the eight last CASES, at

Leisure Hours.

(38) Lent at Christmas 1793, the Sum of 5000/ at 4 per Cent. after which Time I lent several Sums at the same Rate, and drew upon the Borrower, as Business requir ed; viz. on Lady-day 1794, I drew for 185 Guineas; on Midsummer-day following, I lent 500 Moidores, and drew for 700/ and on Michaelmas-day, in the same Year, I lent 569/ 17s. I demand what Cash the Borrower owed me at that Time?

(39) On the first of May 1793, I lent Ralph Newlands, per Bill at one Day's Date, 500, which I received back in the following partial Payments, viz. on the 13th of May 501, on the 4th of June 561, on the 14th of July 44/, on the 23d ditto 50%, on the 18th of August 877, on the 30th ditto 131, on the 21st of September 301, on the 18th of October 30, on the 29th ditto 401, on the 11th of November 501, and on the 28th of December 50%. Now I demand to know what Interest is due at 5 per Cent. per Annum? (40) Lent to John Jameson, per Bill dated 18th of Jan. 1793, payable one Day after Date, 8781 19s 10d, which I received back in the following partial Payments, viz. on the 27th of February, 57/ 15s 7d. on the 18th of March 377 14s, on the 29th of April 34/ 11s, on the 12th of May 1367 15s 7d, on the 19th of June 671 13s 4d, on the 15th of July 15 Guineas and 6d, on the 25th ditto 111/ 11s 11d, on the 3d of Oc

tober 781 7s 4d. on the 19th of November 100%. on the 23d ditto 100%. and on the 30th of December received the Balance of the Principal. How much Interest ought I to claim at 5 per Cent?

(41) Lent 109 Guineas at 4 per Cent. By the 18th of August, 1799, they were raised by the Interest to so many Moidores, abating Half-a-Crown: pray on what Day did the Bond bear Date?

(42) If 100. in 12 Years be allowed to gain 39/ 19s 8d. in what Time will any other Sum double itself at the same Rate of Interest?

(43) A Bond was made on the 7th of August, 1786, at 6 per Cent. per Annum, for 1114/ 10s. On the 11th of May, 1789, 1407. was paid off, and a fresh Bond entered into for the Remainder at 54 per Cent. per Annum ; at the Time the Interest for this last was 21/ 16s 8d. there was paid off 87/ 11s 9d. The old Bond being then taken up, a new one was given for the Residue, which being paid off September 11, 1793, the Bondowner took no more than 1409/ 16s 8d. in full Payment: at what Rate did he take Interest per Cent. per Annum, upon the last Renewal of the Bond? (44) It is proposed by an elderly Person in Trade, desirous of a little Respite, to admit a sober industrious young Fellow in the Business; and to encourage him, offers, that if his Circumstances will allow him to advance 1007. his Pay shall be 401. a Year; if he shall be able to put 2001. into the Stock, he shall have 551. a Year, and if 3007. he shall receive 70%. annually. In this Proposal, what was allowed for his Attendance simply? and what Rate per Cent. was allowed for his Money? (45) June 23d, 1745, bought 900%. of New South-Sea Annuities, at 1113 per Cent. viz. the Day before the closing the Books, the Brokerage whereof is always 2s 6d. per Cent. on the Capital, whether you buy or sell. The Midsummer Dividend 2 per Cent. became due and payable on the 10th of August following; by which Time the Rebellion growing considerable in the North, the said Annuities were down at 924 per Cent. In the general Alarm, sold 4007. Capital at that Price; but continued the Remainder, till a second, third, fourth, and fifth Dividend, as before, came due; and on opening the Books on the 10th of August 1747,

sold out at 1023 per cent. Now, reckoning I might have made 5 per Cent. of my Money, had I kept it out of the Stocks, how stood this Article in point of Profit and Loss?

XIX. COMPOUND INTEREST

IS that which arises both from Principal and its Interest, put together, as the Interest becomes due, but not paid; the same Interest is allowed upon that Interest unpaid, as was upon the Principal; so it becomes a part of the Principal; and for which Reason it is called Interest upon Interest, or Compound Interest.

It is not lawful to let out Money at Compound Interest: yet, in purchasing of Annuities or Pensions, and Leases in Reversion, it is usual to allow Compound Interest to the Purchaser for its Ready Money, and therefore makes it necesthat it should be understood.

sary

But as it may as well as other Cases of Interest be more conveniently performed by Decimals, so shall only give the Rule, and a few Examples.

RULE.

1. Find the first Year's Interest as in Case 1. Add that Interest to the Principal, which Sum will become the second Year's Principal, and so on for any Number of Years.

2. Subtract the given Principal from the last Amount, and the Remainder will be the Interest required.

EXAMPLES.

(1) What is the Compound Interest of 600, forborne 3 Years, at 5 per Cent. per Annum ?

(2) What is the Amount of 1501. for 5 Years, at 4 per Cent. per Annum, Compound Interest?

(3) What is the Compound Interest of 440/ 16s. for 4 Years, 7 Months, and 15 Days, at 5 per Cent. per Annum ? Note. When the Interest is required for Months and Days, besides Years, you must find the Interest for one Year more than the Number of Years given, and, from that Year's