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What is the balance, June 14, 1832 ?
Find the balance due on the following note by the Mas. sachusetts rule.
Hartford, Feb. 1. 1820. Value received I promise to pay A. B. or order, five hundred dollars with interest.
8.00 April 1, 1821,
12.00 May 1, 1821,
30.00 How much remains Sept. 16, 1821 ?
Find the balance dúe on the following note by the Con. necticut rule.
For value received I promise to pay G, B. or order, eight hundred and seventy-five dollars, with interest. $875.00
SAMUEL JONES. Hartford, Jan. 10, 1821.
Aug. 10, 1824, received
July 1, 1827,
The three rules used above, are all considered as ob. jectionable.
By the first rule, when a man pays a part of his debt, his payments are not applied to discharging the interest, but entirely to lessening the principal. By this rule, if
What is the common rule for calcnlating interest on notes when there are endorsements ? the Massachusetts rule ? the Connecticut rule? What are the objections to the three rules?
man should borrow a sum and promise to pay it, with the interest, in twenty-five years, if he should simply pay what would be the yearly interest, and have it endorsed, at the end of 25 years the debt would be entirely extinguished. Whereas if he should wait till the end of the time agreed upon, he would have to pay the original sum borrowed, and the yearly interest upon it also.
The objection to the other two rules is, that the man who makes payments before the time of settlement, actu. ally is obliged to pay more than one who pays nothing before that time. Thus the most punctual man is obliged to pay more than the negligent.
Compound Interest is the only method which will do exact justice to both creditor and debtor. For a man who lends money is fairly entitled to receive interest at the end of each year ; and then by investing the interest in other stock, he can obtain compound interest. The borrower, therefore, who detains this yearly interest, ought, in justice, to pay what the creditor could gain, if the debtor were punctual.
COMPOUND INTEREST. Compound Interest is an allowance made for the use of the sum lent, and also for the use of the interest when it is not paid.
RULE. Calculate the Interest, and add it to the principal at the end of a year. Make the Amount a new principal for the next year, with which proceed as before, till the time of settlement.
1. What is the compound interest of $256 for 3 years, at 6 per cent. ?
What is the only method to do justice to the creditor? What is compound interest? What is the rule for performing it?
$256 given sum, or first principal.
15,36 interest, 256,00 principal,
to be added together.
271,36 amount, or principal for 2d year.
16,2816 compound interest, 2d, year, together
287,6416 amount, or principal for 3d. year.
17,25846 compound interest, 3d. year, 287,641 principal,
A. $48,899 compound interest for 3 years.
2. At 6 per cent. what will be the compound interest, and what the amount, of $1 for 2 years ?
what the amount for 3 years ? for 4 years ?
for 5 years ? for 6 years ? for seven years ?
Ans. to the last, $1,593+ It is plain that the amount of $2 for any given time, will be 2 times as much as the amount of $1 ; the amount of $3 will be 3 times as much, &c.
Hence, we may form the amounts of $1 for several years, into a table of multipliers for finding the amount of any sum for the same time. The following
number of years, not exceeding 24, the rates of 5 and 6 per cent. compound interest.
How is the Table used ?
Y'rs. 5 per cent. 6 per cent.
5 per cent. 11,05 1,06 131,88564+ 2,13292+ 21,1025 1,1236 141,97993+ 2,26090+ 31,15762+ 1,19101+ || 152,07892+ 2,39655+ 41,21550 +1,26247+ || 162,18287+ 2,54035+ 51,27628+ 1,33822+ 172,29201+ 2,69277+ 61,34009-11,41851+ 18 2,40661+ 2,85433+ 71,40710 + 1,50363+ 192,52695+ 3,02559+ 8 1,47745+ 1,59384+ 202,65329+ 3,20713+ 91,55132+ 1,68947+ || 512,78596+ 3,39956+ 101,62889+1,79084+ || 222,92526+ 3,60353+ 111,71033+ 1,89829+ || 233,07152+ 3,81974+ 121,79585+ 2,01219+ 24 3,22509+ 4,04893+
Note 1. Four decimals in the above numbers will be sufficiently accurate for most operations.
Note 2. When there are months and days, you may first find the amount for the years, and on that amount cast the interest for the months and days; this added to the amount will give the answer.
3. What is the amount of $600,50 for 20 years, at 5 per cent. compound interest ? at 6 per cent. ?
$1 at 5 per cent. by the table, is $2,65329; therefore, 2,65329 X 600,50581593,30+ Ans. at 5 per cent. ; and 3,20713 X 600,50=$1925,881+ Ans. at 6 per cent.
4. What is the amount of $40,20 at 6 per cent com. pound interest, for 4 years ?
for 10 years ? for 18 years?
for 12 years? for 3 years and 4 months ? for 24 years, 6 months, and 18 days?
Ans. to last, 8168,137.
Discount is a deduction made from a debt, for paying it before it is due.
If, for example, I owe a man $300 two years hence, and am willing to pay him now, I ought to pay only that
What is discount? What is the rule for performing it ?
sum, which, with its interest, would in two years, amount to $300.
The question then is, what sum, together with its inte. rest at 6 per cent., would, in two years, amount to $300 ?
Such operations are performed by the rule for finding the principal, when the time, rate, and amount are given, (see page 207).
The sum, which, in the time mentioned, would, by the addition of its interest, amount to the sum which is due, is called the present worth.
What is the present worth of $834, payable in 1 yr. 7 mo. 6 days, discounting at the rate of 7 per cent. ?
Ang. $750. What is the discount on $321,63, due 4 years hence, at 6 per cent. ?
Ans. $62,26. What principal, at 8 per cent., in 1 yr. 6 mo. will amount to $85,12?
Ans. $76. What principal, at 6 per cent. in 11 mo. 9 d. will amount to $99,311?
Ans. $94. How much ready money must be paid for a note of $18, due 15 months hence, discounting at the rate of 6 per cent. ?
STOCK, INSURANCE, COMMISSION, LOSS AND
Stock is a name for money invested in banks, in trade, in insurance companies, or loaned to a national government for the purpose of receiving interest.
Persons who invest money thus, are called stockholders.
When stockholders can sell their right to stock for more than they paid, it is said that stock has risen, and when they cannot sell it for as much as they paid, it is said that stock has fallen.
Stock is bought and sold in shares, of from $50 to $100 a share.
What is stoek? When is stock said to have risen or fallen?