LESSON 132. Another common but incorrect method. To obtain what is due on a note or bond when partial payments have been made, many persons, Find the amount of the principal at the time of settlement, also the amount of each payment at the time of settlement, and then subtract the sum of the amounts of the payments from the amount of the principal. This method is easy but illegal, and is considered unjust towards the lender; for if you lend me $100 at 6 per cent., and I pay you the interest, or $6, at the end of every year, in 25 years the amounts of the payments will be more than the amount of the principal. Experiment, however, shows it may be employed without much error, when a settlement is made within a year of the commencement of interest on the note or bond. lt may be used with propriety to find the balance due on an account at interest. Perform the following examples by this rule. 1. Example 4, lesson 131. Ans. $32.08. 2. Example 5, lesson 131. Ans. $110.50. 3. Example 6, lesson 131. Ans. $6.22. 4. What is the balance due on the following account, settled January 1st, 1835; each item drawing interest at 6 per cent. ? Samuel Jay's account with David Sibley, Dr. 1834. Cr. March 1. To Goods $200 1834. $100 85 125 "Goods May 5. Sept. 8. "Pork 66 130 Dec. 20. "Cash Ans. $78.77, due David Sibley. Explanation. The easiest course is to multiply each item on the Dr., or debtor side by the time in days, multiply the sum of the products by the rate, or .06, and divide this product by 365. The quotient is plainly the whole How do many persons obtain what is due on a note or bond, when partial payments have been made? What is said of the ease, legality, and justice of this method? When may it be employed without much error? When also may it be used? interest on the Dr. side. Proceed the same way to get the interest on the Cr., or creditor side. 5. Find the sum due on the following account at interest, settled August 11th, 1838, 7 per cent. being reckoned. R. Leach, his account current with J. Barr. Dr. 1838. Ans. $51.04 due R. Leach. 6. What is due on the following account at interest, settled July 1st, 1830, money being worth 5 per cent. ? John Marsh's account current with James Colburn. 60 April 11." Potatoes 100 Ans. $9.27 due James Colburn. Note. The rule employed in the Courts of New Jersey, is but very little different from that given at the beginning of lesson 131. The rules employed in the Courts of Connecticut and Vermont, produce results a little different from this rule. The following is the rule established by the Supreme Court of the State of Connecticut in 1804, and should be studied by residents in that State. It may be omitted by others. CONNECTICUT RULE. Compute the interest to the time of the first payment; if that be one year or more from the time the interest commenced, add it to the principal, and deduct the payment from the sum total. If there be after payments made, compute the interest on the balance due, to the next payment, and then deduct the payment as above; and in like manner from one payment to another till all the payments are absorbed; provided the time between one payment and another be one year or more. But if any payments be made before one year's interest hath accrued, then compute the interest on the principal sum due on the obligation 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 that sum What is said of the rule employed in the Courts of New Jersey? Of the rules employed in the Courts of Connecticut and Vermont? Recite the Connecticut Rule. from the principal and interest, added as above. However, if the year extends beyond the time of settlement, find the amount of the principal remaining unpaid, up to the time of such settlement, also the amounts of the payment or payments up to the same time, and deduct their sum from the amount of the principal. If any payments be made of a less sum than the interest arisen at the time of such payment, no interest is to be computed, but only on the principal sum for any period. Example 1, lesson 131, is performed by this rule, thus ; Principal, $327.00. Add interest from June 4th, 1829, to April 16th, 1831,. 36.61. Deduct amount of second and third payments, at the end of this year, or April 16th, 1832, . 21,58. 257.85. Add interest on $257.85 to the time of settlement, 11.02. 268.87, Deduct amount of fourth payment at time of settlement,... 55.99. Due January 1st, 1833,... 22 cents less than the answer found by the first method given. $212.88. Explanation. We found the amount of the second and third payments from the time the third payment was made; for when the second payment was made, the interest on the principal sum amounted to more than the payment. COMPOUND INTEREST. LESSON 133. Compound Interest is a reward paid for the principal, and also for the interest after it becomes due. To calculate compound interest, therefore, Make the amount at the time interest is due a new principal, on which cast the interest to the time when interest is again due, and so on, and finally subtract the first principal from the last amount. What is compound interest? How do we calculate compound interest? 1. Suppose I give a note, on demand, for $100, at 6 per cent., and at the end of each year give a new note for the principal and interest; what will all the interest come to in 3 years? OPERATION. $100 principal. .06 6.00 100. 106. amount, principal for the second year. .06 6.36 interest for the second year. 106 112.36 amount, principal for the third year. .06 6.7416 interest for the third year. 112.36 119.1016 amount at the end of 3 years. subtract 100 Note. Instead of multiplying by .06, and adding the principal to the product for the amount, it is plain that we can obtain each amount by multiplying by 1.06. 2. What will $255.16 amount to in 5 years, at 6 per cent., compound interest; the interest being added to the principal in a new note at the end of each year? Ans. $346.59. 3. A man lent $1,000 at 7 per cent., on condition of receiving the interest every 90 days; what will be the whole amount in 1 year 40 days, if all the interest proceeding from this sum be lent on the same terms? Ans. $1,081.24. 4. What will a note for $1,843.12 amount to in 6 years, at 6 per cent., the interest being added to the principal in a new note at the end of each year? Ans. $2,614.51. In example 1, instead of multiplying by .06 and adding the principal to the product for the amount, what course can we take? 5. What will the interest on a note for $1,200 amount to in 3 years, at 6 per cent., the note being renewed every 90 days, and the interest included in it? Ans. $238.33. The following table will enable us to perform examples in compound interest with great ease. TABLE, Showing the amount of $1 at 5, 6, and 7 per cent., compound interest, from one year to 40. |