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PROBLEM I. The principal, time, and rate per cent. given, to find the interest.
RULE. Multiply together the decimal expressing the rate per annum, the time in years and the decimal of a year, and the principal: the product will be the interest.
This problem has already been exemplified in the preceding pages of this article.
PROBLEM II. The principal, time, and amount given, to find the rate per cent. per annum.
RULE. Subtract the principal from the amount, and the remainder will be the interest for the given time. Divide this interest by the given time expressed in years or the decimal of a year, and the quotient will be the interest for one year. Divide the interest for one year by the given principal, and the quotient will be the rate per cent. per annum.
133. At what raie per cent. per annum must 172 dol. lars 40 cents be put on interest, in order to amount to 332 dollars 74 cents, in 5 years
? 134. Lent 51 dollars 25 cents, and in 1 year and 4 inonths it amounted to 55 dollars 35 cents.
What was the rate per cente per annum ?
135. Borrowed 340 dollars for 9 months, and at the expiration of the time it amounted to 355 dollars 30 cents. What was the rate of interest per annum ?
136. At what rate per cent. per annum must 87 } cents be put on interest, in order to amount to 98 cents, in 2 years ?
PROBLEM III. The principal, rate per cent., and amount given, to find the time.
RULE. Subtract the principal from the amount, and the remainder will be the interest. Divide the interest by the principal, and the quotient will be the interest of 1 dollar. Divide the interest of 1 dollar by the rate, and the quotient will be the time.
137. In what time will 89 dollars 25 cents amount to 92 dollars 82 cents, at the rate of 6 per cent. a year?
138. In what time will 171 dollars 40 cents, amount to 231 dollars 39 cents, at 7 per cent. a year?
139. Borrowed 163 dollars 50 cents at 6 per cent. a year; at the time of payment it amounted to 176 dollars 58 cents. How long did I keep the money!
140. In what time will 4810 dollars 25 cents, amount to 5002 dollars 66 cents, at 6 per cent. a year ?
141. Lent 114 dollars at an interest of 7 per cent. a year; on its return it amounted to 127 dollars 30 cents. How long was it out?
142. In what time will $ 100, or any other sum of money double, at the rate of 6 per cent. per annum, simple interest?
PROBLEM IV. The amount, time, and rate per cent. given, to find the principal.
RULE. Divide the amount by the amount of 1 dollar for the time, and the quotient will be the principal.
This problem forms the subject of the next article, under the head of Discount.
DISCount is an allowance made for the payment of money before it is due.
The present worth of a debt, payable at a future period without interest, is that sum of money, which, being put on interest, would amount to the debt, at the period when the debt is payable.
It is obvious, that, when money is worth 6 per cent. per annum, the present worth of $ 1.06, payable in a year, is $1. Hence, the present worth of any debt, payable in a year, is as many dollars as there are times $ 1.06 in the debt. And hence we deduce the following.
RULE. Divide the debt by the amount of 1 dollar for the time, and the quotient is the present worth. Subtract the present worth from the debt, and the remainder will be the discount.
1. What is the present worth of 450 dollars, payable in 6 months, when money is worth 6 per cent. per annum ?
2. What is the present worth of 535 dollars, payable in 15 months, when money is worth 6 per cent. per annum ?
3. When money is let for 6 per cent. per annum, what is the present worth of a note for 1530 dollars, payable in 18 months ?
4. Sold goods to the amount of 1500 dollars, to be paid one half in 9 months, and the other half in 18 months: what is the present worth of the goods, allowing interest to be 5 per cent. per annura?
5. What is the present value of a note for 2576 dol. lars and 83 cents, payable in 9 months, when interest iš 6
per cent. per annuin ?
6. When interest is 6 per cent. a year, what is the difference between the discount on 1285 dollars for a year and 8 months, and the interest of the same sum for the same time?
7. Purchased goods amounting to 6568 dollars 50 cents on a credit of 8 months: allowing money to be worth 4 per cent. a year, how much cash down will
pay the bill ?
8. A man, having a horse for sale, was offered for it 225 dollars, cash in hand, or 230 dollars payable in 9 months: he chose the latter, although money was worth 7 per cent. a year.
How much did he lose by his ignorance?
9. Bought a quantity of goods for 1831 dollars 53 cents cash, and the same day sold them for 1985 dollars 48 cents on a credit of 6 months, when money was 5 per cent. a year. How much did I gain upon the goods ?
10. What is the discount on 198 dollars 60 cents, for 9 months, when interest is 5 per cent. a year?
11. What is the discount on 241 dollars 81 cents, for 7 months, when interest is 4 à per cent. a year ?
12. What is the present worth of 741 dollars 65 cents, payable in 48 days; interest being 6 per cent.?
BANKING A BANK is an institution which trafficks in money. It is owned in shares, by a company of individuals, called stockholders; and its operations are conducted by a President and board of Directors. It has a deposite of specie, and issues notes or bills, which are used for a circulating medium, as money. These bills are mostly obtained from the bank in loans, on which interest is paid; and the amount of bills issued being greater than the amount of specie kept in deposite, a profit accrues to the bank.
The interest on money hired from a bank, is paid at the time when the money is taken out-the hirer receiving as much less than the sum he promises to pay, as would be equal to the interest of what he promises to pay, from the time of hiring the money until the time it is to be paid. From this circumstance, the interest on money hired from a bank is called discount, and the promissory note received at the bank is said to be discounted.
A note, to be discounted at a bank, is usually made payable to some person, who endorses it, and who thereby binds himself to pay the debt, in case the signer of the note should fail to do so. Any person, therefore, who holds the note of another, payable at a future time, may endorse it, and obtain the money for it at a bank, by paying the bank discount; provided the credit of the parties is undoubted.
It is customary in banks, to compute the discount on every note for 3 days more than the time stated in the note; and the debtor is not required to make payment until 3 days after the stated term of time has elapsed. These 3 days are called days of grace.
1. What is the bank discount on 775 dollars for 30 days, and grace, when interest is 6 per cent. a year?
2. What is the bank discount on 900 dollars for 98 days, and grace, at the rate of 6 per cent a vear ?
3. How much is received on a note for 2540 dollars 80 cents, payable in 4 months, discounted at a bank, when interest is 43 per cent. a year?
4. A note for 452 dollars, payable in 7 months, is discounted at a bank, when interest is 6 per cent. per annum. What sum is received on it?
5. A note for 3000 dollars, payable in 70 days, is discounted at a bank, when interest is 6 per cent. a year. What sum is received on it ?
6. A merchant bought 1625 barrels of four for 5 dollars a barrel cash, and on the same day sold it for 5 dollars 50 cents a barrel, on a credit of 8 months, took a note for the aniount, and got it discounted at a bank, when money was 6 per cent. a year. How much did he gain on the flour?
7. A man got his note for $ 1000, payable in 3 months, discounted at bank, at the rate of 6 per cent., and immediately put the money he received for his note on interest for 1 year, at 6 per cent.
He kept the money from the bank 1 year, by renewing his note every 3 months, and paying in the required bank discount at each renewal. At the end of the year he received the amount of the money he had put on interest, and paid his note at. the bank. How much did he lose by this exchange ?
In the above example, interest on the several discounts paid into the bank forms part of the loss.
8. A money broker subscribed for 20 shares in a new bank; at $100 a share. When the bank commenced operation he paid in 50 per cent. of the price of his stock, and in 6 months after, he paid in the remainder. In 12 months from the time the bank commenced, there was a dividend of 31 per cent. on the stock among the stockholders; and the same dividend accrued every 6 months thereafter. At the end of 3 years the broker sold his stock at 7 per cent. advance. Now, allowing that this broker hired his money, and paid 6 per cent. annually how much did he make by the speculation ?
In this example, the broker must charge annual interest on the interest he pays, and must give credit for annual interest on his share of the dividends.