MULTIPLES FOR DAYS.

155

14. Construct the aliquot formulae for 1-12 mos. at the

rates 31, 213.

15. Construct the aliquot formulae for 1-12 mos. at rates from 2 to 3 (by 8ths).

6. Days. Method of Multiples.

Convert money into £ and decimals (to 3 places). Multiply (using methods of prediction, § vi) by the multiplier derived from the table corresponding to the product "days × rate.”

Table of Interest on £1 at 1 p.c.

Example 1.

531.582

9745 300

15947

2658

212

37

5

£1.8859

17s. 8d.

Interest on £531. 11s. 7 d. for 37 days at 34 p.c.
3+3+1=7 places required in the multiplier (§ vi).

Example 2. Interest on £265. 13s. 84d. for 92 days at 21% p.c.

Find Interest on

EXAMPLES.

1. £712. 98. 101d. for 91, 95 days at 31, 21
2. £832. 5s. 8d. for 110, 71 days at 51, 38.
3. £912. 78. 6d. for 85, 94 days at 41, 38.
4. £705. 11s. 41d. for 97, 61 days at 23, 45.
5. £1246. 12s. 5 d. for 125, 93 days at 3g, 4.
6. £3125. 16s. 104d. for 61, 92 days at 23, 5.
7. £973. 14s. 52d. for 87, 95 days at 118, 211.
8. £641. 7s. 11td. for 72, 81 days at 21, 11.
9. £1432. 88. 101d. for 271, 82 days at 33, 15%
10. £495. 19s. 10d. for 91, 87 days at 55%, 11.

16

3

7. Days. The Third, Tenth, and Tenth Rule. Make the denominator 73000.

Find the corresponding numerator.

Move the decimal point in the principal 5 places to the left.

Multiply this principal (thus changed) by the

numerator.

Add to this product of it, then of this, then of this again.

The answer is too great by 10000 (15 per mille).
10 p.m. d. per £10 approximately.

=

Example. Int. on £612. 9s. 54d. for 93 days at 31.

1. £372. 8s. 41d. for 56, 89 days at 31, 416.

2. £712. 98. 7 d. for 167, 312 days at 23, 57.
3. £274. 118. 6d. for 210, 184 days at 4,5%, 1.
4. £195. 17s. 41d. for 95, 91 days at 51, 28.
5. £846. 13s. 7 d. for 34, 147 days at 33, 43.
8. Days. Method of Prediction.
days x rate

Reduce

cancellation.

36500

to a simple fraction without

Decimalise the principal to 3 places and move the decimal point to the left as many places as there are zeros in the denominator of the above fraction.

Then decide by the method of prediction the no. of places which must be correct in the multiplication of the altered principal by the numerator of the fraction so as to ensure correctness to three places in the final answer after division by the denominator (without zeros)—the methods of approximation being employed for the multiplication and division.

Multiply and divide accordingly.

Example 1. £312. 13s. 41d. for 83 days at 3 p.c.

83 × 3

249

=

36500 36500

3.12667 x 249 will contain 3 integers.

365 has 3... there can only be 1 integer in the final answer.

Hence we shall have 4 figures in the answer.

And therefore we must have 4 figures correct in the multiplication, of which 3 are integers--thus we must get 1 place correct in the multiplication.

The argument is put down actually thus:

3.12667 x 249=3 integers.

3 | 3 | 1+3=4-3=1 dec. place required.

Example 2. £851. 178. 3 d. for 173 days at 21 p.c.

Note 1. A rule of thumb for deciding the no. of places necessary is:

Reverse multiplier and place the digit now in the unit-place under the last place but one of the altered principal.

Note 2. This method surpasses all others in speed and convenience.

Other forms of it are given on p. 143.

COMMON METHODS.

EXAMPLES.

159

Find Interest on

1. £653. 9s. 10d. for 129, 83 days at 3, 23 respectively. 2. £234. 11s. 71d. for 91, 94 days at 41, 31 respectively. 3. £412. 16s. 81d. for 87, 32 days at 5, 4 respectively. 4. £516. 148. 101d. for 215, 300 days at 65, 21 respectively. 5. £617.8s. 5td. for 74, 89 days at 7, 3§ respectively. 6. £3125. 98. 74d. for 321, 64 days at 31, 23 respectively. 7. £274. 7s. 81d. for 93, 78 days at 45, 333 respectively. 8. £427. 13s. 4ąd. for 36, 57 days at 1, 23 respectively. 9. £561. 12s. 6d. for 63, 49 days at 111, 3 respectively. 10. £187. 6s. 11 d. for 128, 212 days at 2, 2 respectively. 11. £695. 118. 10d. for 84, 100 days at 31, 43 respectively. 12. £834. 98. 74d. for 75, 92 days at 41, 31 respectively. 13. £721. 48. 103d. for 65, 178 days at 57, 23 respectively. 14. £392. 58. 8d. for 81, 200 days at 311, 5 respectively. 15. £268. 78. 43d. from May 10 to June 13, March 5 to June 8, at 31, 41 respectively.

16. £156. 10s. 71d. for 3 mos. (no grace) from May 12, June 13 at 2, 3 respectively.

17. £647. 158. 32d. for 2 mos. (no grace) from Nov. 6, March 5 at 11, 213 respectively.

18. £318. 14s. 5d. for 4 mos. (no grace) from June 11, May 1 at 31, 4 respectively.

19. £2514. 78. 6d. for 3 mos. (grace) from Nov. 1, 88, May 3 at 51, 211 respectively.

20. £768.12s. 9d. for 2 mos. (grace) from Jan. 1, 89, Feb. 3, 92 at 71, 3 respectively.

9. Common Methods.

A. Reckon 30 days to the month and 360 days to the year-used in America.

Rules based upon this reckoning.

(1) To find the time in years, months and days between two dates.

Reckon the months according to their rank in the and the dates as so many days.

year,

Subtract as for a Table proceeding by 12 and 30.