(2) Any p.c. for any number of years, months, days. Find interest for 1 year and take aliquot parts for the time, treating the years, months, days, separately. Example. £863. 17s. 3 d. at 4 p.c. for 3 years 2 months 5 days. B. Reckon exact no. of days to the month and 360 days to the year-used on the Continent. Any p.c. for any no. of days. Multiply of principal by days x rate 360 Aliquotise the fraction days × rate 360 In this way we get the advantage of the factors of 360, but the interest is too much. = 01369863, hence divide by 73 or multiply by this decimal and subtract to get the absolute interest. Example. Int. on £313. 8s. 4d. for 90 days at 3 p.c. 90 × 3 360 COMPOUND INTEREST. 161 It is very often simpler to deduct at these rates: d. in 1s. 6d., 1d. in 6s., 3s. in £11, £1 in £73. Aliquotation is very simple to the base 360. Note. The American Government and the U. S. Courts reckon 365 days to the year. Many Continental Governments however reckon as in (B). sum of Compound Interest. 10. Compound Interest arises in reality when a money is left to accumulate in banks or (with certain reservations) in government funds. But the actual process of calculation may be said never to be required in such cases, for the practice is at the end of the year to look up the interest on the sum for the year, add it to the principal and enter this as the new principal in the new year's account. The calculation of compound interest does arise however in some very important cases-viz. the determination of annuities, and the calculation of Life Insurance Tables. Hence multiply principal by a similar expression to 104 to get the amount for 1 year and repeat the process according to the no. of years given-to get amount for given no. of years. 1o. To multiply by such an expression as 1·04. Put down principal in decimals to no. of places desirable for accuracy (4 in general to ensure exactness to farthings). Add rate principal, commencing to multiply 2 places to left of final figure on right taken-make allowance in usual way and put the first figure in product under last taken on the right. Repeat process to get amount for given no. of years. Example 1. Compound amount of £729. 8s. 114d. for 3 years at 4 p.c. 2o. When the expression is of the form 1031. Use the same method, but the fraction must be allowed for in a third line each year, i.e. for the fraction divide the top line for the year by the denomr., placing answer two places to the right or divide the second line by the denominator of the fraction similar to 1÷3 -then add as usual. Example 2. Compound amount of £831. 9s. 7 d. for 2 years at 3p.c. 831-4822816 4.1574 860.5842 25.8175 of 2nd line or of 1st line moved two places. 4.3029 890-7046 £890. 148. 1d. ABBREVIATED OPERATIONS. 3°. When the expression is of the form 1021. 163 Then use the same method, but divide the first line for any year by the first aliquot and put answer two places to the right, then use remaining aliquots on this result. Finally add as usual. Example 3. Compound Amount of £642. 18s. 71d. for 3 years at 31% p.c. 318-3-224 1. Compound amount of £732. 11s. 71d. for 3 yrs. at 5 p.c. and for 2 yrs. at 31 p.c. 2. Compound amount of £1182. 9s. 51d. for 2 yrs. at 31 p.c. and for 3 yrs. at 23 p.c. 3. Compound amount of £651. 11s. 4 d. for 4 yrs. at 4 p.c. and for 5 yrs at 1 p.c. 4. Compound amount of £105. 7s. 51d. for 3 yrs. at 21% p.c. and for 2 yrs. at 337 p.c. 5. Compound amount of £312. 138. 61d. for 2 yrs. at 5ğ p.c. and for 4 yrs. at 1}} p.c. 6. Compound interest on £685 for 4 yrs. at 11p.c. and for 3 yrs. at 33 p.c. 4 7. Compound interest on £1820 for 5 yrs. at § p.c. and for yrs. at 3 p.c. 8. Compound interest on £970. 5s. 6d. for 6 yrs. at 21 p.c. and for 4 yrs. at 13 p.c. 9. Compound interest on £860. 4s. for 7 yrs. at 1 p.c. and for 3 yrs. at 41% p.c. 10. Compound interest on £1000 for 4 yrs. at 311 p.c. and for 3 yrs. at 12 p.c. 12. The Formation of Tables. Tables of the compound amounts of £1 at various rates for 1, 2, 3, 4, etc. years are of great use in Annuities and similar calculations. They are formed in this way: Find the compound amount for the 1st year. Then multiply it by given rate, putting unit figure two places to the right and adding in the preceding compound amount as you multiply. If the tables are limited to six places, when that number is reached begin to multiply at the third digit (adding in the overplus of the 2nd digit) from the right and add in the usual way. +687880 4 1.040604 1.051010 1.082856 8 1.477455 9 1.838459 9 1.143390 9 10 1.104622 10 1.628894 10 1.967151 10 1.160541 13. General Formula for Compound Interest. Two principles enable us to arrive at a valuable formula for calculating compound amounts for many years. 1o. The compound amount of any principal = the principal x compound amount of £1 for given rate and |