341,00 second payment, September 17, 1826 37,51 interest to July 17, 1828. 378,51 amount. 99,00 third payment, February 2, 1828. 2,72 interest to July 17, 1828. 101,72 amount. 184,50 378,51 several amounts 101,72 yr. mo. yr. mo. mo, $219,52c. remained due on the bond, July 17, 1828. NOTE.-The preceding rule will answer for short periods of time, but when applied to a long course of years, will be found to be very erroneous. Different rules have been established in the different states relative to the computation of interest on notes, bonds, &c. The following Rule is established for the practice of the Courts in the State of New York. "The Rule for casting interest, where partial payments have been made, is to apply the payment, in the first place, to the discharge of the interest then due. If the payment exceeds the interest, the surplus goes toward discharging the principal, and the subsequent interest is to be computed on the balance of principal remaining due. If the payment be less than the interest, the surplus of interest must not be taken to augment the principal; but interest continues on the former principal until the period when the payments, taken together, exceed the interest due; and then the surplus is to be applied toward discharging the principal, and interest is to be computed on the balance of príncipal as aforesaid.” The following Rule was established by the Superiour Court of Massachusetts in 1821. "Compute the interest on the principal sum, from the time when the interest commenced, to the first time when a payment was made, which exceeds, either alone or in conjunction with the preceding payments, if any, the interest at that time due; add that interest to the principal, and from the sum substract the payment made at that time, together with the preceding payments, if any; and the remainder forms a new principal, on which compute interest, as upon the first principal, and from the amount substract the payment; and proceed in this manner to the time of the judgement or settlement." The following Rule was established by the Superiour Court of Connecticut in 1784. "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 payment 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 from the principal and interest added as above. If any payment 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." 2. A gave B a bond for $2000, dated April 15, 1822, on which are the following endorsements: yr. mo. da. 1 4 2 1 10 June 25, 1829, $645,75, What remained due upon the bond October 15, 1831, interest at 7 per cent.? Ans. $1630,27 NOTE. The preceding sum is worked agreeably to the rule established for the practice of the courts in the State of New York. 3. A note was given June 15, 1829, for $1200, on which the following endorsements were made: June 15, 1830, $1000, December 15, 1830, $200, 0 6 What remained due on the note June 15, 1831, interest at 6 per cent.? Ans. $82,56,4m. NOTE.-The rule established by Massachusetts, is, perhaps, for simplicity and correctness, equal, if not superiour to any. 4. A bond was given February 4, 1825, for $1000, interest at 7 per cent., on which the following payments were made: December 14, 1827, $260, yr. mo. da. 1 1 15 04 15 What remained due on the bond January 24, 1829? Ans. $231,26c. 5. A note was given November 1, 1826, for $1000, interest at 7 per cent., on which were the following endorsements: February 10, 1827, $400, August 6, 1828, $500, What remained due on the note July 10, 1829? Ans. $195, 81,2m. COMPOUND INTEREST. Q. What is Compound Interest? A. Compound Interest is that which arises from the principal and interest, or interest upon interest; the intercst being added to the principal, and continuing in the hands of the borrower, becomes a part of the principal at the end of the stated time of payment. EXPLANATIONS. If $100 be on interest, at 7 per cent. per annum, at the end of a year, $107 will be due to the lender; and this $107 will be the principal for the second year to draw interest, and so on; the principal and interest being added together as the interest becomes due; and it is for this reason that it is called Compound Interest. RULE. Q. How do you find the Compound Interest on any given sum for a given time? A. First find the amount of the given sum for the first year, the same as in Simple Interest, which will be the principal for the second year; then find the amount of this new principal, as before, for the second year, and that will be the principal for the third year, and so on for any number of years; and then substract the given principal from the last amount, and the difference, or remainder, will be the Compound Interest. EXAMPLES. 1. What is the Compound Interest of $100, for 4 years, at 7 per cent.? Ans $31,07,9m. You will readily perceive, that the principle of the rule of working Compound Interest is the same as that of Simple Interest, the only difference is, that in Simple Interest, the interest is reckoned on the sum for the given time, and, in Compound Interest, the interest is reckoned at the end of each year, and added to the principal, and, therefore, becomes a part of the principal upon which interest is reckoned. Thus, $100, for 1 year, at 7 per cent. per annum, is $107, which is the principal for the second year; and the amount of $107 is $114,49c.; 31,07,960100 Com. In. of $100 for 4yr. this is the principal for the third year, and so on. 2. What is the Compound Interest of $400, for 5 years, at 6 per cent.? Ans. $135,29c. 3. What is the Compound interest of $760, for 3 years, at 6 per cent.? Ans. $145,17,2m. 4. What will $500 amount to in 3 years, at 7 per cent. Compound Interest? Ans. $612,52c. 5. What is the Compound Interest of £400, for 4 years, at 6 per cent.? Ans. £104 19s. 9fd. |