5d. 24. LESSON 2. 1817 at 3 qrs. Here as in lesson first we say 1817d. which sum, divided by 12 and by 20, will make £7 11s. 5d. as before ; then the half of this sum, and the half of that half, will be equal to the amount at 3q.: because 2 q. are equal to half a penny, and Iq. is equal to half of 29. OPERATION. PROOF. 29. of 1d. 1817 at 3q. 19. of 29. 908d. 2q. 454 1 12 1362d. 39. • 20 113s. 68. 39. Answer, £5 13 6 3 Answer'£ 5 13s. 6d. 3q. LESSON 3. 1691 at id. 29. In this lesson we say 1691 at 18. makes £ 84 11s. Then 1d. is jy of a shilling and 29. 1 of a penny; that is, the 1 of £ 84 11 and the half of that je will give the answer, viz. £ 10 11 4 2 OPERATION. PROOF. • 2011691 at 1s. 1d. is of 1s.[1691 at 1d. 29. id. of 1s. £84 lls. 29. į of 1d. 140s. 11d. 29. 1 of id. 7 Os. 11d. 70s. • 20 211s. 4d. 29. Answer, £ 10 11s. 4d. 29. LESSON 4. 1881 at 25. 3d. 29. Say 1881 at 20s. = { 1881. Then 2s. is zs of a pound, 3d. ; of 2s. and 2q. of 3d. OPERATION. PROOF. 2s. io of £1 £1881 3d. 1 of 18./1881 at 2s. 3d. 29. 2s. 3d. 1 of 25. 188 2s. 29. of 3d. 23 iOs. 3d. 3762s. 3 18s. 4d. 24. 29. of 3d. 470s. 3d. 785. 4d. 29. Answer, £215 10s. 7d. 29. - 20 4310s. 7d. 29. Answer, $ 215 10s. 78. 29. LESSON 5. 478 at 3s. 2d. 19. OPERATION.' Proof, 2s. To of £1 £478 2d. 5 of 1s. 478 at 3s. 2d. 19. 3s. 1s. of 2s. 47, 16s. 2d. of is. 23 18s. 1434s. 3 198. 8d. 19. of 2d.j 79s. 8d. 9s. 11d. 24. 9s. 11d. 29 19. 5 of 2d. Answer, £76 38. 7d. 29. + 2015238. 7d. 29. Answer, ' 76 38. 7. 29. a pair ? LESSON 6 and 7. What will 568 pairs of mittens come to at 2s. 6d. a pair, and at 3s. 4d. Ans. £71 at 2s. 6d. and €94 135. 4d. at 3s. 4d. EXPLANATION. In the first place we consider 568 pairs at 20s. equal to £ 568. Then as 2s. 6d. is of a pound, we divide by 8, the quotient is the answer at 2s. 6d. Secondly, we say 35. 4d. is of a pound, and divide by 6, the quotient will be the answer at 38. 4d. OPERATIONS. 2s 6d. į of £11568 at 2s. 6d. 38. 4d. of £1|1568 at 3s. 4d. Answer, £71 Answer, £ 94 138 4d. LESSON 8 and 9. 678 at 5s, and at 6s. Bd. OPERATIONS. 55. of £1)678 at 5s. 6s. 8d. į of £1)678 at 6s. 8d. Answer, 169 10s. Answer, €226 LESSON 10. 678 at 78. 6d. 24. DIRECTIONS. Say 678 at 20s.<£ 678. Then take parts of that sum thus: 45.5 of a pound ; 28.=} of 48.; 18.= of 2s.; 6d.=1 of 1s. and 2q=1 of 6d. OPERATION. PROOF. 48. } of 1£. £678 at 7s. 6d. 29. 6d. of 1s.[678 7 2s. į of 4s. 135 12s. 1s. 1 of 2s. 67 16s. 4746s. 6d. į of 1s. 33 18s. 29. le of 6d. 339s. 16 19s. 18./678 28s. 3d, 1 8s. 3d. · 2015113s. 3d. Answer, £255 138. 3d. Answer, £255 13s. 3d. LESSON 11. 459 at 15s. 8d. 39. Here we will suppose that 459 cost £459. Then say, 10s.=} of a pound ; 58.5 of 10s.; 6d.= 1 of 58.; 2d.= of 6d. ; 29.= of 2d. and 19.= of 29. OPERATION. PROOF. 10s. į of 1£. 1459 at 15s. 8d. 39. 6d. of 1s. 459 х 3 1377 2d. of 6d. 11 98. 6d. x 5 29. of 2d. 3 16s. 6d. 19. of 29. 0 198. id. 2q. 6885s. 9s. 6d. 39. 2d. 4 of 6d. 229s. 6d. 24. of 2d. 769. 6d. Answer, £360 198. 8d. 19. 19. 1 of 29. 198. 1d. 27. 29. 1 of 6d./ 9s. 6d. 3q. 20172195. 8d. 19. Answer, € 360 195. 8d. 17. LESSON 12. 642 at 37s. 6d. 29. STATEMENT. Say 642 pounds; this will include the amount of the integers at 208. each: then for 175. 6d. 29. say 10s.=į of a pound; 58.=the half of 108.; 25. 6d.=the half of 5s. and 24.=és of 2s.6d. OPERATION. PROOF. 10s. of 1£. £642 6d. I of 1s.1642 15.1642 58. of 10s. 321 x 378. 2s. 6d. I of 5s. 160 10s. 29. do of 2s. 60 80 58. 4494 1 6s. 9d. 1926 Answer, 1205 1s. 9d. 24. i's of 6d.) 3215 23754s. 20124101s. 9d. Answer, £ 1205 ls. 9d. LESSON 13. What cost 15 tons 9 cwt. 3 qrs. 25 lb. of iron, at £2 168. a hundred ? Answer, £867 188. 6d. DIRECTIONS. 1. Multiply the price of 1 cwt. by 20, the product will be the price of 1 ton. 2. Multiply the price of 1 ton by 15, the product will be the price of 15 tona. 3. Multiply the price of 1 cwt. by 9, the product will be the price of 9 cwt. 4. For the 3 qrs. 25 lb. say, 2 qrs.=1 of 1 cwt.; 1 qr.=) of 2 qrs.; 14 lb. = of 1 qr.; 7 lb.=1 of 14 lb.; and 4 lb.= part of 1 cwt. OPERATION. 2 qrs. of 1 cwt.[£2 16s. price of 1 cwt. 1 4 £ 840 Os. price of 15 ton. € 2 16s. x 9 = 25 4 price of 9 cwt. 11 4 1 qr. of 2 qrs. 1 8. price of 2 qrs. 5 141b. of 1 qr. 14 price of 1 qr. 7lb. of 141b. 7 price of 141b. Price of 1 ton, 56 0 3 6d. price of 71b. 3 4lb.= as of 1 cwt. 2 Od. price of 41b. $ 8400 Proof in dollars and cents, at the rate of 8s. to the dollar. 2 yrs. of 1 cwt./87. cwt.18% price of 1 cwt. cwt. 1 ton. $ 2169.8125 Answer, $ 2169.814 cents. INTEREST. LESSON 1. Suppose a note was given on interest April 2, 1813, and paid March 4, 1816; how many years, months, and days does it draw interest ? Answer, 2 years 11 mo. and 2 days. OPERATION. 1816 years 2 mo. 4 days. 1813 3 2 2 Answer, 11 2 Allow 30 days to be 1 month and 12 months 1 year. OBSERVATIONS. 1. The Note was paid on the 4th of March 1816, which time we call 1816, years on New-year's day last before the payment, and the 4th of March we say is 2 months and 4 days after New-year's day. 2. So again for the time of signing the note, we say that the 2nd of April was 3 months and 2 days after New-year's day 1813. Subtract and carry at 30 and at 12. APPLICATION. What is the interest of a Note of $ 450.75 for 2 years 11 mo. and 2 days at 7 per cent. per annum? Answer, $ 92.20+ DIRECTIONS. First, find the interest for three years ; then take one twelfth of one year's interest from that sum, the difference will be 2 years 11 mo. interest. Secondly, take the 15th part of one month's interest for 2 days. OPERATION. 45075 cents. 7 per cent. 3155.25 one year's interest. the time. 9465.175 three years' interest. 262.93 one month's interest subtracted. 9202.182 two years' and 11 months'interest. 17. 528 two days' interest or 15th of 1 mo. 9220.1348 Answer, $ 92.20 cents, and .348 + thou sandths of a cent. LESSON 2. OPERATION. 1817 years, 2 mo. 2 days. 1812 4 5 27 4 9 APPLICATION. What is the amount of $16.50, for 4 years, 9 months and 27 days, at 7 per cent. per annum ? Aps. 822.07+ OBSERVATIONS. 1. In this case obtain the interest for 4 years; then lake half the interest for 1 year, and the half of that half for 9 months. 2. For 27 days, divide the interest of 1 year by 12, the quotient will be the interest of 1 month, viz. 9.6250 cents; subtract to of a month's interest, that is 3 days, from that sum, the remainder will be 27 days' interest, viz. 8.6625 cents. OPERATION. 109.6250 1 month. 6 mo. 4 a yr.)115]50 interest for 1 year. .9625 3 days. 8.6625 27 days. 462100 interest for 4 years. 3 mo. of 6) 57 75 interest for 4 a year. 28.875 interest for of a year. 557|2875 interest for 4 years, 9 mo. 27 days. 2207|2875 amount, or answer. COMPOUND INTEREST, CALCULATED BY LOGARITHMS. RULE. Add the rate per cent. to 100; find the Logarithm of that sum, and subtract from it the Logarithm of 100; call the difference, Logratio ; multiply the Logratio by the number of years, and to that product add the Logarithm of the principal; the natural number of the last Logarithm will be the amount in Compound Interest. EXAMPLE 1. What is the amount of $500 for three years, at 7 per cent. per annum, compound interest ? Ans. $612.50 2.00000 Logratio or difference, 0.02938 3 x Product, 0.08814 [Continued. |