52. In what time will 100 dollars, or any other sum of money, double itself, at 6, 7, 8, or any other rate per cent. per annum, simple interest? RULE. As the rate per cent. is to one year, so is 100 dollars to the number of years it will be in doubling itself; or, divide 100 dollars by the rate per cent. and the quotient is the time. Ans. 16 years at 6 per cent. 142 years at 7 per cent. per cent. 53. In what time will 340 dollars 25 cents amount to 626 dollars 6 cents, at 7 per cent. per annum ? Ans. 12 years. 54. In what time will 650 dollars amount to 910 dollars, Ans. 5 years. at & per cent. per annum ? A TABLE shewing the number of days, from any day in any month, to the same day in any other month, throughout the year. Jan Feb Mar Apr]May]June]July] Aug]Sept Oct Nov Dec Jan. 365 334306| 275 | 245 153 123 92 62 181 151 120 90 212182 151 121 273 242 212 181 151 304 273243212|182 334 | 303 273 242212 365 334 304 | 273 | 243 31 365 335 304 274 304 245 215 184 212 243 334 304 151 120 92 61 31 365 335 July 181150 122 91 61 80 365 31 92 61 61 30 365 334 304 92 61 91 365 335 Dec. 91 61 30365 Use of the Table.-Suppose you want to know the number of days between the 8th of May, and the 8th of November following. Under the column of May, at the top of the table, look for November in the left-hand column, and you will have 184 days. Again, how many days from the 4th of March, to the 4th of September following? Look in the top column for March, and in the left-hand column for September, and run your finger along, until you come to the column headed March, and you will find 184 days. And if it be required to find how many days there be from 14th June, to the 20th April, you must find how many days there are, first from the 14th of June to the 14th of April, which you will find to be 304 days; then add the number of days from the 14th to the 20th June, which is 6, to 304, and it will make 310 days. If the days in the given months be different, their difference must be added to, or subtracted from the number found in the table. Thus, from the 14th of June to the 20th of April, is 304+6=310 days; and from the 20th April to the 14th June, is 61 days, less 6, equal 55 days. If the time exceeds a year, 365 days must be added for each year. Calculating interest on bonds, notes, &c. RULE 1. Find the interest of the principal from the time the interest first commenced, to the time of the first payment, and add the interest thus found to the principal, and subtract from the whole the payment made, and the remainder forms a new principal, on which proceed as you have done, till all the payments are brought in. By this rule, when a payment alone, or in conjunction with any preceding payment, is less than the interest then due, no calculation is to be made, but these lesser payments added to the next. Therefore no part of the interest ever forms, or becomes a part of the principal bearing interest, the payments being first applied to discharge the interest. There are other methods used, which I will give examples of; but the above one is the best. EXAMPLE. 55. A passed his note to B for 800 dollars, dated the first of January, 1823, payable in four years, with interest from the date, at 6 per cent. per annum, on which A paid the following sums, viz. 1823, July 1st, paid on said note $100 1823, Nov. 1st, paid 1824, Jan. 1st, paid 1824, Sept. 1st, paid 1825, Sept. 1st, paid 1826, April 1st, paid 150 100 80 100 150 $680 paid. What was the balance due on A's note, on the first day of January, 1827? K Principal at interest from Jan. 1st to July 1st, 1823 Six months interest $800 00 24 00 Balance due, the new principal Interest on said balance, up to 1st Nov. (4 months) The new principal, bearing interest 588 48 5 88+ Interest on said balance, up to Jan. 1st, 1824, (2 months) The new principal, bearing interest Interest on said new principal, to Sept. 1st, (8 months) Due first of September, 1824 . The new principal, bearing interest · 80 00 434 13 Interest on said new principal, to Sept. 1, 1825, (12 months) 26 04+ The new principal, bearing interest Interest on said new principal, to April 1, 1826, (7 months) Interest on said new principal, to Jan. 1, 1827, (9 months) 10 02+ Another method, used by merchants. RULE 2. Multiply the principal by the number of days, till the first payment is made, and the remaining principal by the number of days between the first and second payments, &c. till all the payments are made; then add all these products together, and divide the whole sum by 60, and the quotient will be the answer, or interest in cents. This divisor 60 will do when the rate is at 6 per cent. This 60 is found by dividing 6 into 365 days. A divisor for 5 per cent. is found by dividing 365 by 5=73, &c. The above question performed by this rule. NOTE. The column above, containing the interest of the several balances is calculated by Compound Proportion. The divisor 60 is not correct, because 365 divided by 6 gives 605 as a quotient. But multiply 365 days by 100 dollars = 36500 ÷ 6 — 6083+ for a divisor, which will give the quotient in dollars. Thus, RULE 3. As 100 dollars, with 365, is to 6 per cent, so is the different balances, with their number of days, to their respective interests. RULE 4. Multiply the number of days into the balances at interest, add their products together, and divide that sum by 6083, and the quotient will be the answer in dollars, that is, the interest, which, added to the balance of principal due, will be the whole amount due. Another method. RULE 5. When the time is months, or months and days between each payment, multiply each sum by the months it is at interest, and take the quotient of 1200, divided by the rate per cent. as a divisor. Thus, for 6 per cent. the divisor is 200, for 5 per cent. 240, for 8 per cent. 150, &c. RULE 6. Find the interest on the principal, from the time the interest commenced, to the time of settlement, and add it to the principal, and likewise the interest on each payment, from the time the payment was made, to the time of the settlement, and add the several interests to their respective payments, and deduct the whole amount from the amount of the note, bond, &c. and the remainder is the balance due on the note, &c. |