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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, are 220 days; to November the 24th, are 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.
Suppose August 8th, then from
There remains the number of days, viz.
- 365 days,
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, - 309 days, Subtract that answering to May 9,
The remainder is the number of days sought, viz. 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,
Remains the number to the end of the year,
The sum is the number of days required, viz.
And thus is the number of days readily found for any interval of time given, in the same year completely; or which one, and part of another year.
(29) What is the interest of 2001. for 73 days, at 3 per cent. per annum?
(30) What is the amount of 3401. 10s. from January 1, 1789, to July 18 following, at 5 per cent. per annum ? (31) What is the interest of 500l. 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.
1. Say, As the amount of 100l. at the rate and time given is to 100l.:: 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.
(32) What principal, being put to interest for 9 years, at 4 per cent. per annum, will amount to 856/. 10s.?
(33) What principal, being put out to interest for 7 years, will amount to 614. 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.
Say, As the interest of the principal for a year is to 1 year so is the whole interest; to the time required.
(34) In what time will 600l. amount to 8561. 10s. at 4 per cent. per annum?
(35) In what time will 4987. 6s. 8d. amount to 6147. 3s. 11d. at 3 per cent. per annum?
Case 9. When the principal, amount, and time are given, to find the rate per cent.
1. Say, As the principal is to the interest, for the whole time so is 100l. 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.
(36) At what rate per cent. per annum will 600l. amount to 856/. 10s. in 9 years?
(37) At what rate per cent. per annum will 498l. 6s. 8d. amount to 614l. 3s. 11d. in 72 years?
QUESTIONS for Exercise in the last Eight CASES, at leisure Hours.
(38) Lent at Christmas 1804, the sum of 5000l. at 4 per cent. after which time I lent several sums at the same rate, and drew upon the borrower, as business required; viz. on Lady-day 1805, I drew for 185 guineas; on Midsummer-day following, I lent 500 moidores, and drew for 700l. and on Michaelmas day, in the same year, I lent 5691. 17s. I demand what cash the borrower owed me at that time.
(39) On the first of May 1805, I lent Ralph Newlands, per bill at one day's date, 500l. which I received back in the following partial payments; viz. on the 13th of May 507. on the 4th of June 567. on the 14th of July 447. on the 23d ditto 50l. on the 18th of August 871. on the 30th ditto 137. on the 21st of September 307. on the 18th of October 30l. on the 29th ditto 401. on the 11th of November 50l. and on the 28th of December 501 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. 1805, payable one day after date, 878/ 19s. 10d. which I received back in the following partial payments; viz. on the 27th of February 577. 15s. 7 d. on the 18th of March 377, 14s. on the 29th of April 34l. 11s. on the 12th of May 136l. 15s. 7d. on the 19th of June 671. 13s. 4d. 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 100l. on the 23d ditto 100l. 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 100l. in 12 years be allowed to gain 397. 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 11141, 10s. On the 11th of May, 1789, 140l. was paid off, and a fresh bond entered into for the remainder at 5 per cent. per annum; at the time the interest for this last was 217. 16s. 8d. there was paid off 871. 11s. 9d. The old bond being then taken up, a new one was given for the residue, which being paid off September 11, 1796, the bond-owner took no more than 14091. 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 man in the business; and, to encourage him, offers, that if his circumstances will allow him to advance 1001. his pay shall be 40l. a year; if he shall be able to put 2001. into the stock, he shall have 55l. a-year, and if 3001. he shall receive 70l. 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 9001. of New South-Sea annuities, at 1113 per cent. viz. the day before the closing the books, the brokerage of which 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.
general alarm, sold 400l. capital at that price; but continued the remainder, till a second, third, fourth, and fifth dividend, as before, came due; and on openF
ing the books on the 10th of August 1747, sold out at 102 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 his ready money, and therefore makes it necessary that it should be understood.
But as it may (as well as other cases of interest) be more conveniently performed by decimals, I shall only give the rule, and a few examples.
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.
(1) What is the compound interest of 600l. forborne 3 years, at 5 per cent. per annum?
(2) What is the amount of 150l. for 5 years, at 4 per cent. per annum, compound interest?
(3) What is the compound interest of 440l. 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