SECOND METHOD. The following was established as a standing rule, by the superior court of the State of Connecticut, in 1784, for computing interest on notes or obligations, as before stated: 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 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 before. 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. A note, dated August 11th, 1824, given for $750, at 6 per cent. per annum, (as in the last example,) and the indorsements as follows: February 11th, 1826, $300; November 26th, 1826, $200; July 16th, 1829, $ 250; how much is due on said note, August 16th, 1830? Ans. $156 Note, METHOD OF OPERATION. Interest up to first payment, it being 1 year, 6 months, Amount, new principal, Interest for 1 year, (a payment having been made before 1 year's interest had accrued,) dolls. 750.00 2d payment, dolls. 200.00 Int. to end of the year, it being 2 months, 16 days, 2.52 202.52 202.52 new principal, T 3d payment, it being 2 yrs. 5mo. 5 days, Amount, new principal, Int. up to time of settlement, it being lyr. Îmo. 250.00 dolls. 156.00 Due on the note, according to this method, Note, the second payment being made before one year's interest had accrued, the interest, according to rule, must be computed on the principal sum, (or new principal,) for 1 year; that is, from February 11th, 1816, the time of the last payment, to February 11th, 1817, which is 2 months, 16 days; this interest add to the payment, and then subtract it from the principal added above. The operation I have left for the learner to work out. have put down the time, it will be better for him to find it. THIRD METHOD. Although I The courts of law, in Massachusetts, established the following rule for computing interest on notes, &c. on which partial payments have been indorsed: RULE. 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 payment, (if any,) the interest at that time due; add that interest to the principal, and,from the sum, subtract the payment made at that time, together with the preceding payment, (if any,) and the remainder forms a new principal, on which compute and subtract the payments, as upon the first principal, and proceed in this manner, to the time of final settlement. EXAMPLE. The example the same as before, viz. a note dated August 11th, 1824, given for $750 at 6 per cent. per annum. Indorsements as follows: February 11th, 1826, $300; November 26th, 1826, $200; July 16th, 1829, $250; how much is due on this note, August 16th, 1830? Ans. $155.68cts. Note, METHOD OF OPERATION. Interest up to first payment, it being 1 year, 6 months, Dolls. 750.00 Interest up to 2d payment, it being 9 mo. 15 days, new principal, Interest up to 3d payment, it being 2yrs. 7mo. 20 days, Interest up to time of settlement, it being 1 year, 1 month, Dolls. 155.68 Due on the note, according to this method, The following is the balance due by each method, as exemplified in the examples. Annuities, Pensions, &c, in Arrears at Simple Interest. Note. An annuity is a yearly income arising from money, &c. and is payable yearly, for a certain number of years, or for life, and when a person keeps the annuity in his own hands beyond the time of payment, it is said to be in arrears. The sum of the annuities for the time they have been forborne, together with the interest, due on each, is called the amount. If an annuity is bought off, or paid for, all at once at the commencement of the time, the price paid is called the present worth. Annuities are generally payable or due, either yearly, half yearly, or quarterly. Here, let A, represent the amount; R, the ratio of rate per cent. and T, the time as before. Note, U, represents the annuity. That is, time mult. by the ann. mult. by time, less the time and ann. The result divided by 2, and the quotient mult. by the ratio, to which add time and ann. the sum is equal to the amount. EXAMPLES. 1. If an annuity of 80£ be forborne 5 years, what will be due for principal and interest, at the end of said term, simple interest, being computed at 6 per cent. per annum? Ans. £448 TUT TU R TU £ 5x80×5-400÷2 ×.06+400-448 the amount, Observe, TU is the time and annuity multiplied together. From the rule and what is above, I think the learner may find the result of the fol. lowing questions. 2. Suppose a house be let upon a lease of 8 years, at $200 per annum, and the rent be in arrears for the whole term; what is due at the end of said term; simple interest being allowed, at 5 per cent. per annum? Ans. 1880 Dolls, Note, when the annuity, &c. is to be paid half yearly or quarterly, then for half yearly payments, take half of the ratio, half the annuity, &c. and twice the number of years; that is, reduce the years to half yearsand for quarterly payments, take a fourth part of the ratio, and a fourth part of the annuity, and four times the number of years, and work as before. 3. If a salary of 100£, payable every half year, remains unpaid for 5 years, what will it amount to in that time, at 6 per cent. per annum? Ans. 567£ 10s. Half the ratio will be .03; half the annuity, 50; the number of half years, 10; work as before. 4. If the payment of a pension, due quarterly, be omitted to be paid for 5 years, what will it amount to in that time, if 5 per cent. be allowed to a person who has a pension of $200? Ans. $1118.75cts. The fourth part of the ratio will be .0125, for that is the fourth of .05; the ann. 50; and the quarter years, 20; proceed as before. PRESENT WORTH OF ANNUITIES. Here, P represents the present worth, U T and R as before. To find the present worth of an annuity, at simple interest. Given, U, annuity; T, time; and R, ratio; to find P, present worth. 1. How much present money is equal to an annuity of $ 200, to continue 5 years, at 6 per cent.? = Ans. 861D. 53cts. 8m, RTT RT 2T .06 X 5 X 5 - 30 + 10 11.20 the dividend. .06 X 5 X 2 + 2 = 2.60 the divisor; divide the dividend by this divisor, and multiply the quotient (4.30769) by (200) the annuity, the product will be the answer. 2. What is the present worth of 60£ per annum, to continue 4 years, at 5 per cent.? Ans. 214£ 19s. 11d. 3qrs. + NOTE. The same is to be observed here for half yearly and quarterly payments, as mentioned in the last rule. 3. What is a pension of 250 dolls. per ann. worth, in ready money, payable half yearly, at 6 per cent. for 5 years? Ans. 1091dolls. 34cts. 6m. + Take half the ratio; half the pension; and double the years; and pro ceed according to rule. 4. What is the present worth of a pension of 60dolls. per annum, payable quarterly, for 5 years, at 6 per cent? Ans. 263dolls. 65cts. 3m. + Take the fourth of the ratio; one fourth of the annuity; and 4 times the number of years, &c. COMPOUND INTEREST. The following letters are made use of, viz. A, the amount; P, the principal; T, the time; R, the ratio or the amount of 1£ or $1, for a year; and is found by the following proportion: as 100: 105 :: 1 :: 105, ratio at 5 per cent. or, As 100: 106 :: 1.06, ratio at 6 per cent. &c. 1 Table of the amounts of 1£ for a year. Rate Am't of Rate Am't. of Rate Am't of Rate Amt' of The rule explained, is thus; P, principal, multiplied by the ratio involved so many times, as the number of years direct is equal to the amount. NOTE.-Subtract the principal from the amount, the remainder will be the compound interest. EXAMPLE FOR ILLUSTRATION. 1. What is the amount of 500 dollars, for 4 years, at 6 per cent.? Ans. 631D. 23cts. 8m.+ According to the rule, the ratio must be involved into the time, and that product multiplied by the principal, as follows: R R R R D. cts. m. 1.06X1.06X1.06 X 1.06-1.26247696X500-631.23848000-631.23 8 + Observe, When the time is 4 years involve the ratio 4 times; when 5 years, 5 times, &c. P D. 2. What is the amount of 2481. 10s. for 5 years, at 5 per cent. per annum? Ans. 3171. 3s. 1d. 1qr, and rem. Proceed according to rule, and involve the ratio 1.05, five times and multiply the product by the principal; mind and reduce the 10s. to cimal |