TABLE, Showing the amount of $1, or £1, at 3, 4, 5, 6, and 7 per cent. com interest, for any number of years, from 1 to 40. 2.500,080 3.373,133 32. 2.575,083 3.508,059 33. 2.652,335 3.648,381 34. 2.731,905 3.794,316 35. 2.813,862 3.946,089 36. 4.538,039 6.088,101 8.14 2.898,278 4.103,933 5.791,816 8.147,252 11.4 37. 2.985,227 4.268,090 6.081,407 8.636,087 12.2 38. 3.074,783 4.438,813 6.385,477 39. 3.167,027 4.616,366 40. 3.262,038 4.801,021 9.154,252 13.0 6.704,751 9.703,507 13.9 427. To calculate compound interest by the preceding table. Find the amount of $1 or £1 for the given number of years by the table, multiply it by the given principal, and the product will be the amount required. Subtract the principal from the amount thus found, and the remainder will be the compound interest. 6. What is the compound interest of $500 for 15 years, at 6 per cent.? What is the amount? Operation. $2.396558 Amt. of $1 for 15 yrs. by Table. $1198.279000 Amt. required. $500 Principal to be subtracted. $698.279 Interest required. 7. What is the amount of $960 for 10 yrs., at 7 per ct.? 8. What is the amount of $1000 for 9 yrs., at 5 per ct.? 9. What is the compound int. of $1460 for 12 yrs., at 4 per ct.? 10. What is the compound int. of $2500 for 15 yrs., at 6 per ct.? 11. What is the amount of $5000 for 20 yrs., at 6 per ct.? 12. What is the amount of $10000 for 40 yrs., at 7 per ct.? DISCOUNT. 428. DISCOUNT is the abatement or deduction made for the payment of money before it is due. For example, if I owe a man $100, payable in one year without interest, the present worth of the note is less than $100; for, if $100 were put at interest for 1 year, at 6 per cent., it would amount to $106; at 7 per cent., to $107, &c. In consideration, therefore, of the present payment of the note, justice requires that he should make some cbatement from it. This abatement is called Discount. 429. The present worth of a debt payable at some future time without interest, is that sum which, being put at legal interest, will amount to the debt, at the time it becomes due. QUEST.-428. What is discount? 429 What is the present worth of a debt, payable at some future time, without interest? Ex. 1. What is the present worth of $756, payable in 1 year and 4 months, without interest, when money is worth 6 per cent. per annum? Analysis. The amount, we have seen, is the sum of the principal and interest. (Art. 399.) Now the amount of $1 for 1 year and 4 months, at 6 per cent., is $1.08; (Art. 404;) that is, the amount is 108 of the principal $1. The question then resolves itself into this: $756 is 108 of what principal? If $756 is 108 of a certain sum, is of $756; now $756÷108=$7, and 100-$7X100, which is $700. Or, we may reason thus: Since $1.08 (amount) requires $1 principal for the given time, $756 (amount) will require as many dollars as $1.08 is contained times in $756; and $756÷$1.08= $700, the same as before. PROOF.-$700.08=$56, interest for 1 year and 4 months; and $700+56=$756, the sum whose present worth is required. Hence, 430. To find the present worth of any sum, payable at a future time without interest. First find the amount of $1 for the time, at the given rate, as in simple interest; then divide the given sum by this amount, and the quotient will be the present worth. (Art. 404.) The present worth subtracted from the debt, will give the true discount. OBS. This process is often classed among the Problems of Interest, in which the amount, (which answers to the given sum or debt,) the rate per cent., and the time are given, to find the principal, which answers to the present worth. 2. What is the present worth of $424.83, payable in 4 months, when money is worth 6 per cent.? What is the discount? Solution.-$424.83-$1.02 $416.50, Present worth. And $424.83-$416.50=$8.33, Discount. 3. What is the present worth of $1000, payable in 1 year, when the rate of interest is 7 per cent.? 4. What is the present worth of $1645, payable in 1 6 months, when the rate of interest is 7 per cent.? year and QUEST.-430. How do you find the present worth of a debt? How find the discount? 5. What is the discount on a note for $2300, payable in 6 months, when the rate of interest is 8 per cent.? 6. What is the discount, at 6 per cent., on $4260, payable in 4 months? 7. What is the present worth of a note for $4800, due in 3 months, when the rate of interest is 6 per cent.? 8. What is the present worth of a draft for $6240, payable in 1 month, when the rate of interest is 6 per cent.? 9. A man sold his farm for $3915, payable in 24 years: what is the present worth of the debt, at 6 per cent. discount? 10. What is the present worth of a draft of $10000, payable at 30 days sight, when interest is 6 per cent. per annum? 11. What is the difference between the discount of $8000 for 1 year, and the interest of $8000 for 1 year, at 7 per cent.? BANK DISCOUNT. 431. A Bank, in commerce, is an institution established for the safe keeping and issue of money, for discounting notes, dealing in exchange, &c. OBS. 1. There are three kinds of banks, viz: banks of deposit, discount, and circulation. A bank of deposit receives money to keep, subject to the order of the depositor. This was the primary object of these institutions. A bank of discount is one which loans money, or discounts notes, drafts, and bills of exchange. A bank of circulation issues bills, or notes of its own, which are redeemable in specie, at its place of business, and thus become a circulating medium of exchange. Banks of this country generally perform the three-fold office of deposit, discount, and circulation. 2. The affairs of a bank are managed by a board of directors, chosen annually by the stockholders. (Art. 392. Obs.) The directors appoint a president and cashier, who sign the bills, and transact the ordinary business of the bank. A teller is a clerk in a bank, who receives and pays the money on checks. A check is an order for money, drawn on a banker, or the caslier, by a depositor, payable to the bearer. 3. Banks originated in Italy. The first one was established in Venice, in 1171, called the Bank of Venice. QUEST.-431. What is a bank? Obs. Of how many kinds are banks? 432. It is customary for Banks, in discounting a note or draft, to deduct in advance the legal interest on the given sum from the time it is discounted to the time it becomes due. Hence, Bank discount is the same as simple interest paid in advance. Thus, the bank discount on a note of $106, payable in 1 year, at 6 per cent., is $6.36, while the true discount is but $6. (Art. 430.) OBS. 1 The difference between bank discount and true discount, is the interest of the true discount for the given time. On small sums for a short period this difference is trifling, but when the sum is large, and the time for which it is discounted is long, the difference is worthy of notice. 2. Taking legal interest in advance, according to the general rule of law, is usury. An exception is generally allowed, however, in favor of notes, drafts, &c., which are payable in less than a year. The Safety Fund Banks of the State of New York, though the legal rate of interest is 7 per cent., are not allowed by their charters to take over 6 per cent. discount in advance on notes and drafts which mature within 63 days from the time they are discounted.* Banks charge interest for the three days grace. CASE I. 12. What is the bank discount on a note for $850.20 for 6 months, at 6 per cent.? What is the present worth of the note? Operation. $850.20 Principal. .03 05 Int. $1 for 6 mo. 3 ds. grace. 4251 00 25 5060 $25.9311 00 Bank discount. And $850.20-$25.93=$824.27, Present worth. Hence, 433. To find the bank discount on a note or draft. Cast the interest on the face of the note or draft for three days more than the specified time, and the result will be the discount. The discount subtracted from the face of the note, will give the present worth or proceeds of a note discounted at a bank. QUEST.--432. How do banks usually reckon discount? What then is bank discount? Obs. What is the difference between bank discount and true discount? Is this difference worth noticing? How is taking interest in advance generally regarded in law? What exception to this rule is allowed? * Revised Statutes of New York, (3d edition,) Vol. I. p. 741. |