The 6d. subtracted make the correction spoken of, they proceed from the total sum of pounds, for the interest of the 23 days; this sum is of 202£. of which striking off the units, we have taken the third of the 20 tens, and count them as pence, which is the same as if we had taken the 7200th part of 202.*

*For in the first place by taking the third of the lens, we divide them by 3. 2dly. If we counted them for units of pounds, they would then be thrice ten times or 30 times fmaller; then to count them as fhillings, they must again be divided by 20, which makes them twenty times thirty times, or fix hundred times fmaller; In fine, to be brought to pence, this laft value must be divided by 12, which makes them 7200 times fmaller.

But this number is to be divided by 100; it is then 100 times too great; the result obtained by this division is then equal to the one we should have by taking the 72nd part of the true number. Thus, for instance, the 72nd part of 36, which is, is the same with the 7200th part of 3600, which is 100 times greater than 36.

Whenever then you have an interest to find out for a number of days, reduce this number into months of 30 days, and parts thereof. But forget not to make the above mentioned correction.

10th. What is the interest, at 4 per cent, of 300£. from the 12th of June exclusively, to the 15th of February inclusively.

6 months 2 do.

£.

300

4

1200 £. interest for 1 year.

600

200

6 days 2 do.

The interest for a certain number of days can also be found by the compound rule of three; for, the preceding question can be expressed thus:

If 100£. during 365 days, give 4£. of interest, how much will give 300£. during 248 days? then we have the proportion 100 × 365: 4£.:: 300 × 248 :x=8£. 02d.

3s.

This result differs a little from the preceding, because in the correction we have paid no regard to the 72nd part of the units of pounds shillings and pence, which ought to have been also subtracted, to render the correction perfectly exact; but this difference is so trifling, that the first method is often preferred to the second, as being shorter, especially when the interest comprises, at the same time, years, months, and days, or only months and days.

PROOF.

There is another method, besides the one just given, which in many cases will perhaps be more expeditious, and in all cases may serve to prove the former. It is as follows:

6

When the interest of any sum, for any time, is at per cent, per annum. Multiply the principal by half the time in months, and divide by 100, (because the interest for 2 months is 1;) if these be days, take for them such part or parts of the principal as half the days are of 30; making for the interest so found, the correction above mentioned. If the days exceed 30, bring them into months of 30 days each, and make the correction for the total.

After having found the interest at 6 per cent. increase or diminish it by proportional parts thereof for any other

rate: as,

11th. What is the interest of 827 £. 18s. 101⁄2d. for 1 year 11 months and 20 days, at 6 per cent. per

12th. What sum will 674£. 13s. 84d. amount to in 5 years 11 months and 28 days, at 6 per cent. per annuin ? Ans. 917£. 6s. 1d.

13th. What is the interest of 517£. 15s. 42. for one month, at 6 per cent. per annum ? Ans. 2£. Ms. 94d.

14th. What is the interest of 327 £. 10s. at 6 per cent. per annum, for 210 days? Ans. 11£. 6s. 1d.

15th. Tell the interest of 240£. for one year and 135 days, at 7 per cent, per annum? Ans. 23£.

Os. 3d.

16th. What is the interest of 371£. for 1 year and 213 days, at 5 per cent, per annum? Ans. 29£. 7s. 6d.

17th. What is the interest of a bond for 325 £, 15s. 6d. for 1 year and 73 days, at 4 per cent. per annum? Ans. 15£. 12s. 9d.

18th. What sum will a bond of 435 £. 13s. 531. amount to in two years 8 months and 19 days, at 3 per cent. per annum ? Ans. 471£. 4s. 2d.

19th. What interest is due on a legacy of 517£. 12s. 84. for 3 years 11 months and 26 days, at 2 per cent per annum ? Ans. 41. 5s. 8d.

CONTRACTIONS.

When the time is

any

number of years, of months separately or collectively, and the rate at 5 per cent.

per annum.

Take of the principal for the interest for 1 year.

20

The reason of this process is obvious, since we have the proportion, 1005: the principal; the interest for one year, and making the reduction 20: 1: the principal: &c. Having in this manner obtained the interest for one year, you will, by the given method, find it for any number of years and months.