Ex. A dividend has accrued from Nov. 11, 1887 to May 15, 1888. Tax changed from 7d. to 6d. on Ap. 5, 3. Mental or very brief methods. (1) 5 p.c. p.a. for a year-divide by 20 (£ as s.). For any no. of years or months multiply by the no. or take aliquot parts of a year. To convert any other rate to 5 p.c.-double the rate and divide by 10 or take aliquot parts of 5. 1 p.c.2 x 5 p.c. 31 p.c.65 × 5 p.c. Ex. Any p.c. p.a. for a year 1 of £ as s. x twice rate. 10 1 Any p.c. p.a. for a month of £ as d. x twice rate. For any no. of years or months multiply by the no. or take aliquot parts of a year. 200 × 6, 150 × 8, (2) The joint factors of 1200 are:-1200 x 1, 600 × 2, 400 × 3, 300 × 4, 240 × 5, 120 × 10, 100 × 12, 80 × 15, 75 × 16, 48 x 25, 40 × 30. 60 × 20, 50 × 24, Hence when the product of the rate x time in months comes to any of the above numbers (small or large) to obtain the Interest divide the Principal by the factor to which it is attached. Ex. 1 p.c. for 4 mos. 1 × 4= 5. divide by 240, 8 p.c. for 5 mos. 8x5=40 .. divide by 30, 3 p.c. for 4 mos. 3 x 4 = 12. divide by 100. The Principal should be decimalised, SIMPLE INTEREST. 151 (3) Similarly in the rare cases when years are involved (unclaimed dividends, etc.) the joint factors of 100 may be employed, viz.:-100 × 1,50 × 2, 25 × 4, 20 × 5, 10 x 10. Ex. 5 p.c. for 10 yrs. 5 x 10-50 .. divide by 2, 12 p.c. for 8 yrs. 12 × 8 =100.. divide by 1. Example 1. Interest at 31 p.c. for 4 mos. on £312. 17s. 44d. Example 2. Int. on £815. 7s. 6d. at 5 p.c. for 5 mos. 1. £512 at p.c. for 1 year, 3, 7, 8 mos. 2. £650 at 5 p.c. for 1 yr., at 3 p.c. for 1 month, at 4 p.c. for 3 mos. 3. £875. 10s. at 3 p.c. for 4 mos., at 4 p.c. for 1 yr. 4. £724 at 2p.c. for 4 mos., 3 p.c. for 5 mos. 5. £1000 at 14 p.c. for 3 mos., 24 p.c. for 4 mos. 6. £7642. 5s. 8d. at 4 p.c. for 1 month, 31⁄2 p.c. for 2 mos. 7. £912 at 7 p.c. for 1 month, 6 p.c. for 4 mos. 8. £8635. 78. 6d. at 6 p.c. for 2 mos., at 5 p.c. for 9 mos, 9. 10. £540. 6s. 9d. at 5 p.c. for 10 mos., at 6 p.c. for 11 mos. £1020. 178. 6d. at 3 p.c. for 7 mos., at 41 p.c. for 8 mos. £250 at 2 for 10 yrs., £5000 at 5 p.c. for 8 yrs. 12. £350 at 14 for 4 yrs., £800 at 10 p.c. for 10 yrs. 11. 4. General Method for Years and Months. Find interest at given rate for 1 year or any no. of years. Take aliquot parts for the time remaining. Example. £731. 8s. 7 d. at 3 p.c. for 3 yrs. 7 mos. 1. £834. 98. 74d. for 4 yrs. 8 mos. at 3p.c. 5. Months. The Method of Aliquotation. When the time is given in months, very often the aliquotation of the product "rate x time" gives surprisingly brief results. The rule to be observed is :— Decimalise the principal to 3 places. ALIQUOTS FOR MONTHS. 153 Aliquotise the product "rate x time" and use the aliquots to multiply and divide the altered principal in the ordinary way. Add and change decimal to s. d. f. Example 1. Int. on £315. 7s. 4d. for 5 mos. at 3 p.c. Ratex time=×{}=255=1=1}=1-444 (aliquot notation). Thus working is 3.15366 .78841 •19710 ⚫04928 Interest= £4.18845 3s. 9d. Example 2. Int. on £712. 9s. 34d. for 3 mos. at 21 p.c. It is obvious that this method is very short if the aliquot formulae are known, and these may be constructed for any commonly-occurring rates for 1, 2, 3 etc. up to 12 mos. The examples given below illustrate such tables. (To be done by constructing the Aliquot Formulae.) 1. £865. 7s. 111d. for 3 mos. at 11, 2 mos. at 15, 7 mos. at 49. 2. £72. 9s. 7d. for 5 mos. at 21, 7 mos. at 3, 10 mos. at 13. 3. £512. 13s. 41d. for 11 mos. at 41, 1 mo. at 73, 10 mos. at . 4. £657. 9s. 43d. for 9 mos. at 31, 3 mos. at 5, 6 mos. at 118. 5. £802. 11s. 51d. for 4 mos. at 21, 7 mos. at 79, 8 mos. at 33. 7. £738. 6s. 1d. for 8 mos. at 4, 3 mos. at 51, 6. £1002. 8s. 7d. for 3 mos. at 51, 8 mos. at 21, 7 mos. at 418. 4 mos. at 35. 8. .£905. 10s. 4d. for 9 mos. at 71, 11 mos. at 13, 8 mos. at 18. 9. £89. 138. 63d. for 7 mos. at 218, 9 mos. at 4, 10 mos. at 43. 10. £1012. 198. 81d. for 6 mos. at 31, 2 mos. at 51, 5 mos. at 93. 11. Construct the aliquot formulae for 3 mos. at 3 and 7 mos. at 41. 12. Construct the aliquot formulae for 1-12 mos. at 53, 231. 13. Construct the aliquot formulae for 1-12 mos. at 63, 31. |