12. What is the interest of $5789 for 29 mo. 29 da.? 13. What is the interest of $80.32 for 7 mo. 19 da.? 14. What is the interest of $175 for 1 mo. 17 da.? 15. What is the interest of $326 for 8 mo. 23 da.? 16. What is the interest of $27.96 for 1 yr. 3 mo. 13 da.? 17. What is the amount of $578.31 for 3 yr. 7 mo. 28 da.? 18. What is the amount of $724.16 for 7 yr. 2 mo. 11 da. ? 19. What is the amount of $4369.87 for 3 mo. 26 da. ? 20. What is the amount of $25.50 for 9 mo. 27 da.? 21. What is the amount of $117.58 for 3 yr. 1 mo. 18 da. ? 22. What is the amount of $313.27 for 6 mo. 9 da.? 23. What is the amount of $57.75 for 9 mo. 1 da.? 24. What is the amount of $35.86 for 11 mo. 25 da.? 25. What is the amount of $17.64 for 1 yr. 1 mo. 13 da.? 26. What is the amount of $378.51 for 1 yr. 5 mo. 17 da.? 175. Computation of Time, and Application to Problems. (a.) In business transactions, it is usually necessary to compute the time during which money has been on interest; that is, the time between the dates on which interest began and ended. (b.) The usual method of doing this is to reckon the number of entire years, then the number of entire calendar months remaining, and then the remaining days. (c.) The year is (as before) regarded as 360 days, or 12 months of 30 days each, and each entire calendar month as a month of 30 days; but the days which are left after reckoning the years and months are determined by counting them according to the number in the months in which they occur. 1. What is the time from Jan. 17, 1845, to June 28, 1849? Solution.-From Jan. 17, 1845, to Jan. 17, 1849, is 4 years; from Jan. 17 to June 17 is 5 months; from June 17 to June 28 is 11 days. Therefore the required time is 4 yr. 5 mo. 11 da. 2. What is the time from April 27, 1846, to Feb. 13, 1851? Solution.-From April 27, 1846, to April 27, 1850, is 4 years; from April 27, 1850, to Jan. 27, 1851, is 9 months; January having 31 days, there are 4 days left in it, which, added to the 13 in February, give 17 days. Therefore the required time is 4 yr. 9 mo. 17 da. 3. What is the time from Sept. 24, 1849, to March 20, .1852? Solution. From Sept. 24, 1849, to Sept. 24, 1851, is 2 years; from Sept. 24, 1851, to Feb. 24, 1852, is 5 months; 1852 being leap year, February has 29 days; hence, there are 5 days left in it, which, added to the 20 in March, give 25 days. Therefore the required time is 2 yr. 5 mo. 25 da. NOTE. This method of computing the time, though the one usually adopted by business men when interest is computed for months and days, is unequal in its operation; for the calendar months, though varying in length from 28 to 31 days, are all reckoned as months of 30 days each. Hence, the interest of a sum during the month of February will be as much as during either March or April, though February contains 3 days less than March, and 2 less than April. By this method, the interest on four notes dated respectively on the 28th, 29th, 30th, and 31st of any one month, and paid on any one day between the 1st and 28th of March, of any year except leap year, would be computed for the same time. Suppose, for instance, that they are dated in October, 1850, and paid March 15, 1851. Then for the first note dated Oct. 28, the time will be found without difficulty to be 4 mo. 15 da. In calculating the time on the others, we proceed thus: Since there are not as many as 29 days in February, 1851, we reckon from the 29th, 30th, or 31st of October to the last day of February as 4 months, to which adding the 15 days in March gives 4 months and 15 days as the time, in each case. The restriction with reference to notes paid in leap year is necessary simply because February has then 29 days. The proposition will always be true of notes dated on the 29th, 30th, and 31st, of any month, and paid at any time between the 1st and 28th of March. Again. Four notes dated respectively on the 28th, 29th, 30th, and 31st of August of any year except the one immediately preceding leap year, and payable in 6 months, would all become due on the same day. The only strictly accurate method of reckoning time is to actually count the days in each month we consider. Thus, to reckon the time from October 28, 1850, to March 15, 1851, we proceed as follows: From October 28th to 31st, is 3 days; to which adding the 30 days in November, the 31 in December, the 31 in January, the 28 in February, and the 15 in March, gives 138 days as the true time between the two dates. In England the time is always computed in this way, as it is in this country when notes are payable at the end of a certain number of days. 4. What is the time from June 23, 1850, to June 3, 1852 ? Answer. 1 yr. 11 mo. Il da. 5. What is the time from May 13, 1847 to Oct. 8, 1851 ? 6. What is the time from Jan. 31, 1851, to March 23, 1852 ? 7. What is the time from Nov. 17, 1849, to Dec. 12, 1851? 8. What is the time from Dec. 31, 1848, to July 6, 1850? What is the interest 9. Of $787.36 from May 3, 1843, to Dec. 17, 1845? 10. Of $54.76 from Feb. 14, 1840, to June 2, 1844? 11. Of $476.35 from June 30, 1847, to Dec. 28, 1850? 12. Of $638.29 from May 31, 1851, to Oct. 7, 1852 ? 13. Of $4937.56 from Dec. 19, 1843, to Feb. 16, 1847? 14. Of $481.74 from Jan. 29, 1847, to March 25, 1851? 15. Of $587.60 from Jan. 31, 1850, to July 18, 1852? What is the amount 16. Of $947.84 from May 15, 1850, to June 13, 1851 ? 17. Of $748.67 from Dec. 14, 1849, to May 4, 1851 ? 18. Of $1546.61 from April 9, 1847, to June 1, 1851? 19. Of $917.68 from June 5, 1842, to Jan. 1, 1850? 20. Of $8396.58 from April 30, 1847, to March 22, 1850? 21. Of $1449.13 from Dec. 31, 1850, to March 5, 1852? 22. Jan. 15, 1852, George W. Pratt borrowed $237.50 of A. N. Johnson, and Feb. 13, 1852, he borrowed $438.75 more, agreeing to pay interest at 6 per cent per year. He paid the debts March 8, 1852. What was their amount? 23. I have three notes against Arthur Sumner, viz., one for $548.17, dated Jan. 1, 1851, another for $679.18, dated Jan. 27, 1852, and another for $376.89, dated May 31, 1852. What amount will be due on all of them July 8, 1852 ? 24. Jan. 1, 1851, I borrowed $3468, with which I purchased flour at $6 per barrel. I sold the flour March 17, 1851, for $6.50 per barrel, cash. Interest being reckoned at 6 per cent, did I gain or lose by the transaction, and how much? 176. Interest by Days. (a.) Many business men always reduce the time to days, and compute the interest by the method illustrated below. As a general thing, however, this method is not so convenient as the preceding. (b.) Since, at 6 per cent per year, the interest for 1 day is of of the principal, it follows that the interest for any number of days must be as many thousandths of the principal as there are days. (c.) We may, therefore, find the interest for any number of days, by multiplying the principal by of the number of days, and removing the point three places farther to the left. It will make no difference with the result, whether we multiply by of the number of days, or by the number of days and divide by 6; but it will usually be bette. to divide before multiplying. 1. What is the interest of $437.62 for 4 mo. 3 da.? Solution. Since 4 mo. 3 da. = 123 da., the required interest must be of 123 of the principal, which is .020 of the principal. The work carried to mills would be written thus: $437.62 8.752 .218 $8.970 Ans. 2. What is the interest of $54.57 for 4 mo. 20 da.? 177. Interest by Dollars, for Months and convenient Parts of a Month. (a.) We can frequently compute interest with great ease by first finding the interest for 1 day, 1 month, or 1 year, and getting the required interest from this. (b) When the interest for any of the above times is any convenient sum, as 1 dollar, 1 dime, 1 cent, 1 mill, dollar, dollar, &c., the proposed course will be particularly advantageous. (c.) Since, at 6 per cent per year, the interest of any sum for 1 month is ʊ of that sum, 1. The interest of $200 is $1 per month. 2. The interest of $20 is $.10, or 1 dime per month. 3. The interest of $2 is $.01 per month. 1. What is the interest of $200 for 7 mo. 15 da.? Solution. The interest of $200 is $1 per month; therefore for 7 mo. 15 da., or 71⁄2 mo., it must be 7 dollars, or $7.50. What is the interest of $200 for What is the interest for each of the above-mentioned 14. What is the interest of $100 for 7 mo.? Solution. Since the interest of $200 is 1 dollar per month, the interest of $100 must be a half dollar per month, and 7 half-dollars, or $3.50, for 7 months. What is the interest of $100 for 15. 9 mo.? 20. 3 mo. 15 da.? |