A table like this can be calculated by finding the amount of $1, at 5, 6 and 7 per cent., compound interest, for 1, 2, 3, &c. years; that is, by multiplying $1 by 1.05, 1.06, 1.07, and the product by the same multipliers, and so on. See note to example 1. 6. What is the compound interest on $50 for 30 years, at 7 per cent. ? Ans. $330.61. Explanation. What will $1 amount to in 30 years, at 7 per cent., by the table? Then what will $50 amount to ? 7. What will the compound interest on $216 come to in 19 years, at 6 per cent. ? Ans. $437.53. 8. What will $18 amount to in 29 years 3 months, at 5 per cent., compound interest? Ans. $75.02. Explanation. What does $1 amount to in 29 years? What does this sum amount to in 3 months? 9. What will $11 amount to in 39 years, at 6 per cent., the interest being added to the principal in a new note at the end of every year? Ans. $106.74. 10. What will the compound interest on $20.25 come to in 12 yrs. 2 mo. and 14 d., at 6 per cent.? Ans. $21. DISCOUNT. LESSON 134. but 1. A dealer in carriages has a chaise marked $195, offers to make a discount or deduction of $23; what sum Ans. $172. will purchase the chaise ? How can a table like this be calculated? 2. A bookseller demanded $17.50 for Irving's works handsomely bound, but concludes to discount 12 per cent., for immediate payment; what is his cash price for the works? Ans. $15.40. 3. If you owe a man $500, to be paid in 2 years, without interest, what must you pay now to cancel the debt, if money is worth 7 per cent. ? Ans. $438.60. Explanation. It is plain that you must pay a sum, which at 7 per cent. interest will amount to $500 in 2 years. The sum to be paid now may be considered as the principal, and $500 as the amount. You have therefore the rate, time, and amount given to find the principal. See rule in Interest, middle of lesson 130. The principal which will amount to a debt, not on interest, when it is payable, is called the present worth of that debt. The difference between the debt and present worth, is the proper discount to be made for immediate payment. 4. What is the present worth of a note for $385 to be paid in 3 years without interest, money being worth 6 per cent. Ans. $318.18. 5. A country trader bought $1,850.37 worth of goods of a merchant of Philadelphia, on 6 months' credit; what discount should the merchant make for immediate payment, if money is worth 6 per cent. ? Ans. $53.89. Explanation. Get the present worth first. 6. What is the present worth of a note for $9,825 to be paid in 276 days, if money is worth 7 per cent. ? Ans. $9,331.09. 7. If you give a man one note for $400, not bearing interest, to be paid in 1 year, and another for $2,537.55, not bearing interest, to be paid in 2 years and 8 months, what sum must you pay down to cancel both of these notes, 6 per cent. being the legal rate? Ans. $2,564.90. 8. A merchant paid $875 down for goods, and sold them the same day for $983.334, on 9 months' credit; what did he gain, money being worth 10 per cent. ? Ans. $39.73. 9. If you are offered $3,000 down for a house, or $3,300 to be paid in 2 years, without interest, which will be the best bargain, money being worth 6 per cent. ? Ans. $3,000 down is the best bargain. Explain how example 3 in Discount should be performed. What is called the present worth of a debt? What is the proper discount to be made for immediate payment? 10. A hardware dealer sold me a stove for $28.50, discounting 5 per cent. from the ordinary price for ready money; what was the ordinary price? Ans. $30. Explanation. See Percentage, example 10, lesson 121. BANKING. LESSON 135. A bank is an institution which trades in money. It is usually owned in shares by persons called stockholders, who choose a President and Directors to manage its concerns. The principal object of a bank is to make and lend notes, called bank bills, as money. When money is borrowed from a bank, the usual manner of proceeding is as follows. If A wants $1,000 for a certain time, say 90 days, and his friend B is willing to become his surety, he writes a note promising to pay B. at the bank $1,000 in 90 days; B now indorses the note, that is, writes his name on the back, thereby making himself a security for the payment. A then proceeds to the bank, and the officers, if they choose, discount the note, that is, they take it, cast the interest on $1,000 for 3 days more than the time, or 90 days, and deducting it from $1,000, hand A the balance in bills. The 3 days are called days of grace, and the bank does not require the $1,000 to be paid until the end of 93 days. Interest paid in this way is improperly called discount. It is plain, then, that banks take interest for larger sums than they lend, and by calling 30 days 1 month, 60 days 2 months, 90 days 3 months, or of a year, &c., obtain interest for a longer time than the borrower has the money. 1. Interest being 6 per cent., what sum do I get on a note for $683, payable in 60 days, which a bank discounts for me? Ans. $675.83. Explanation. Remember the 3 days of grace. What is a bank? How is it usually owned? What is the principal object of a bank? When money is borrowed from a bank what is the usual manner of proceeding? What are the 3 days called, and when does the bank require the note to be paid? What in banking is called discount? What is plain? 2. What is the amount of the bank discount on the following note, interest being reckoned at 7 per cent.? $3,327.40. New York, April 20th, 1837. Ninety days from date I promise to pay James Carver or order, at the Mechanics' Bank, three thousand three hundred and twenty-seven dollars and, for value received George Stilman. Ans. $60.17. 3. A merchant bought $10,000 worth of cotton at $50 a bale, and sold it immediately at $60 a bale, obtaining a note for the amount of the sale, payable in 90 days, without interest; what will be the amount of his gain, if he gets the note discounted at a bank, 6 per cent. being the rate of interest ? Ans. $1,814. 4. How much did a man receive on a note for $982, payable in 70 days, which he had discounted at a bank, where the rate was 7 per cent.? Ans. $968.06. 5. What is the bank discount on a note for $2,500, payable in 4 months, the rate of interest being 6 per cent.? Ans. $51.25. 6. What is the bank discount on a note for $700, payable in 90 days, where the legal rate of interest is 7 per cent.? Ans. $12.66. 7. How much do I receive on a note for $2,000, payable in 30 days, which I get discounted at a bank, the rate of interest being 6 per cent.? Ans. $1,989. 8. I have a note due me for $100, payable in 60 days, which the officers of a bank are willing to discount if I indorse it; what will the discount amount to, 6 per cent. being the rate of interest? Ans. $1.05. EQUATION OF PAYMENTS. LESSON 136. 1. A merchant owes a trading company the following notes. One for $8,480, due in 1 year, without interest, one for $1,526, due in 18 months, without interest, and one for $1,326, due in 21 months without interest; in what time can these debts be paid at once, and neither party sustain loss, reckoning any per cent., say 6? Ans. 1 yr. 1 mo. 24 d., about. Explanation. We first find the present worth of each of these notes, and then find in what time the sum of these present worths amounts to the sum of the debts. This time is evidently the answer. Therefore, to find the time when several debts, due at different times, can be paid at once without loss to either debtor or creditor, Find the present worth of each of the debts, and then find in what time the sum of these present worths will amount to the sum of the debts. This time will be the answer. 2. A merchant sold a country trader a quantity of goods, which were to be paid for as follows; $2,500 were to be paid in 4 months, $350 in 6 months, and $1,000 in 8 months; in what time can all these sums be paid at once, without loss to either party? Ans. in 5 mo. 6 d., about. 3. I bought goods to the amount of $10,067, agreeing to pay $2,300 at the end of 3 months, $2,575 at the end of 6 months, $2,600 at the end of 8 months, and $2,862 at the end of 12 months; it was afterwards thought best that the whole amount should be paid at once; how long after the purchase should the payment be made? Ans. 7 mo. 17 d., about. Other Questions concerning the Payment of Debts. 4. If you owe a man a note for $80, on demand, with interest, and three other notes not drawing interest, one for $16, due in 2 months, one for $25, due in 3 months, and one for $40, due in 6 months, what sum must you pay at the end of 4 months to discharge the whole, 7 per cent. being the legal interest? Ans. $162.74. Explanation. A note not on interest is considered as drawing interest as soon as it becomes due; this being understood, we find the amount of $80 for 4 months, of $16 for 2 months, of $25 for 1 month, and the present worth of $40 Explain how example 1 in Equation of Payments is performed. How do we find the time when several debts, due at different times, can be paid at once without loss to either debtor or creditor? When is a note, not on interest, considered as drawing interest? |