$100 THE SAME QUESTION. Principal 800 dollars, and four years interest 192 dollars. Paid 1st July, 1823 RULE 7. When payments are made in shorter periods than a year, that is, in 4, 6, 7, 8 months, &c. from each other, find the interest on the principal sum for one year, add it to the principal, and compute the interest on the sum paid, from the time it was paid, up to the end of the year, add it to the sum paid, and deduct it from the principal and interest, added as above. If any payment be made of a less sum than the interest due at the time of such payment, no interest is to be calculated, but only on the principal sum, for any period. New principal brought over $493 50 One year's interest on 493 dolls. 50 cts. to 1st Jan. 1825 80 29 61 Amount 523 11 Paid 1st Sept. 1824 81 60 New principal 441 51 26 49 One year's interest on 441 dolls. 51 cts. to 1st Jan. 1826 RULE 8. Multiply the several balances into the days they are at interest then multiply the sum of these products by the rate on the dollar, and divide the last product by 365, the days in a year, and you will have the whole interest due, &c.. THE SAME QUESTION. By the second rule, the sum of the several balances, multiplied into the number of days they were at interest, is By Rule 1, due on said note, § 232 80+ Rule 2, Rule 8, Rule 4, 219 84 218 46 218 48 By Rule 5, due on said note, $218 55 Rule 6, Rule 7, Rule 8, NOTE. I have here given eight examples, by which interest on notes, where partial payments are made, is computed. The first rule is most in use, and is allowed to be the most just; yet there is a great difference between it and all the rest, save the seventh. I cannot inform the scholar, whether there is or not in this state, a rule established by law for calculating interest on bonds, notes, &c. where partial payments are made; but in some of the New England states there is.. COMPOUND INTEREST Is when the interest is added to the principal for one, or at the end of a year, and that sum becomes a new principal for another year, and the interest thereof added again, &c. for any number of years. This is called Compound, or interest upon interest. RULE 1. Find the interest for one year, and add it to the principal, which is the amount for one year. Find the interest of that amount, which add as before, for the amount of the second year, and so on for any number of years. Subtract the original principal from the last amount, and the remainder will be the compound interest for the whole time. RULE 2, by the table. Multiply the figures standing against the number of years by the given principal, and the product is the amount required, from which, if you subtract the principal, the remainder is the compound interest. RULE 3, by the table. Multiply the given principal continually by the amount of one dollar for one year, at the rate per cent. given, until the number of multiplications is equal to the given number of years, and the product will be the amount required, from which, if you subtract the given principal, the remainder will be the compound interest. Yrs.15 per cent.6 per cent.|| Yrs.15 per cent.16 per cent. 1 1,05000 1,06000 11 1,71034 1,89829 23456789 1,10250 1,12360 12 1,79585 2,01219 2,13292 2,26090 2,07893 2,39655 2,54727 7 1,40710 1,50363 17 2,29201 2,69277 10 1,55132 1,68947 19 2,52695 3,02559 1,62889 1,79084 20 2,65329 3,20713 By this table, compound interest may be more expedi tiously calculated, in which the amount of one dollar for any number of years, not exceeding 20, is shewn, at 5 and 6 per cent. per annum, compound interest. Look in the left-hand column for the given number of years, and run your eye along towards the right hand, under 5 or 6 per cent. (as the question demands,) and you will find the number sought. 1. How much is the compound interest of 200 dollars for 4 years, at 6 per cent. per annum? Operation by Rule 2. Tabular number for 4 years, at 6 per cent. 1,26247 200 Amount 252,49,4,00 Principal 200 Answer $52,49,4 Operation by Rule 3. Tabular number for 1 year, 1,06000=1,06 Ans. $52,49,5 2. How much is the amount of 500 dollars for 3 years, at 6 per cent. per annum, compound interest? Ans. 595 dollars 50+ cents. 3. Required the compound interest of 100 dollars for 3 years, at 6 per cent. per annum ? Ans. 19 dollars 10+ cents. 4. What is the amount of 750 dollars for 4 years, at 6 per cent. per annum, compound interest ? Ans. 946 dollars 85+ cents. 5. How much will 650 dollars amount to in 20 years, at 6 per cent. per annum, compound interest? Ans. 2084 dollars 63+ cents. 6. What is the compound interest of 100 dollars for 11 years, at 6 per cent. per annum? Ans. 89 dollars 82 cents 9 mills. 7. What is the amount of 425 dollars 75 cents for 3 yrs: at 6 per cent. per annum, compound interest? Ans. 507 dollars 7+ cents. 8. How much is the amount of 300 dollars for 4 years, at 5 per cent. per annum, compound interest. Ans. 364 dollars 65 cents. 9. A father left 6000 dollars at compound interest, at 6 per cent. per annum, to be equally divided among three sons, when the youngest, who was 12 years of age, should arrive at 21. What will be each son's share then ? Ans. 3378 dollars 94 cents each. NOTE. The ratio is the simple interest of one dollar for one year, at any proposed rate per cent. and is thus found. As 100 : 5 :: 1 to 0,05 ratio. As 100 : 6 :: 1 to 0,06 ratio. The table is constructed in the following manner. To find the tabular numbers, say, As 100 : 105 :: to 1,051,05000 tabular number. As 100 : 106 :: 1 to 1,06 1,06000 tabular number. If the pupil does not wish to work by the tabular numbers, he must make a stating for every year in the question, as in simple interest. COMMISSION, INSURANCE & BROKERAGE. Commission is an allowance of so much per cent. to a correspondent, for buying and selling goods for his employer, and is performed the same as interest for a year. RULE. Multiply the given sum by the rate per cent. and divide the product by 100; or cut off two figures to the right hand, and all to the left will be dollars. |