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675, 00 note, dated April 17, 1793.
884, 25 amount of the note.
$219, 52 remains due on the note, June 17, 1798. 2. On the 16th of January, 1795, I lent James Paywell 500 dollars, on interest at 6 per cent. which I received back in the following partial payments, as under, viz. 1st of April, 1796
$50 16th of July, 1797
400 1st of Sept. 1798
60 How stands the balance between us, on the 16th November, 1800 ?
Ans. due to me $63, 18cts. 3. A PROMISSORY NOTE, VIZ: £62 10s.
New-London, April 4, 1797. On demand I promise to pay Timothy Careful, sixtytwo pounds, ten shillings, and interest at 6 per cent. per
, annum, till paid; value received. JOHN STANBY,
PETER PAYWELL. RICHARD TESTIS. Indorsements.
£. s. 1st. Received in part of the above note, September 4, 1799,
50 0 And payment June 4, 1800,
12 10 How much remains due on said note. the fourth day of December, 1800 ?
Ans. 912 6
NOTE.-The preceding Rule, by custom is rendered so popular, and so much practised and esteemed by many on account of its being simple and concise, that I have given it a place : it may answer for short periods of time, but in a long course of years, it will be found to be very errone
Although this method seems at first view to be upon
the ground of simple interest, yet upon a little attention the Following objection will be found most clearly to lie against it, viz. that the interest will, in a course of years, completely expunge, or as it may be said, eat up the debt. For an explanation of this, take the foilowing
A lends B 100 dollars, at 6 per cent. interest, and takes his note of hand; B does no more than pay.
A at every year's end 6 dollars, (which is then justly due to B for the use of his money) and has it endorsed his note. At the end of 10 years B takes up his note, and the sum he has to pay is reconed thus : The principal 100 dollars, on interest 10 years amounts to 160 dollars ; there are nine endorsements of 6 dollars each, upon which the debtor claims interest; one for 9 years, the second for 8 years, the third for 7 years, and so down to the time of settlement: the whole amount of the several endorsements and their interests, (as any one may see by casting it) is 870,20 cts. this subtracted from 150 dols. the amount of the debt, leaves in favor of the creditor, 889,40 cts. or $10, 20 cts, les, than the original principal, of which he has not received a cent, but only its annual interest.
If the same note should lie 20 years in the same way: B. would owe but 37 dols. 60 cts. without paying the least fraction of the 100 dollars borrowed.
Extend it to 28 years, and A the creditor would fall in debt to B, without receiving a cent of the 100 dollars which he lent him. See a better Rule in Simple Interest Dy decimals, page 175.
COMPOUND INTEREST, Is when the interest is added to the principal, at the end of the year,
and on that amount the interest cast for another year, and added again, and so on : this is called Interest upon Interest.
RULE. Find the interest for a year, and add it to the principal, which call the amount for the first year, find the interest of this amount, which add as before, for the amount of the second, and so on for any number of years required. Subtract the original principal from the last amount, and the remainder will be the Compound Interest for the whole time,
LXAMPLES. 1. Required the amount of 100 dollars for 3
years per cent. per annum, compound interest ?
$ cts. 1st Principal 100,00 Amount 106,00 for 1 year. 2d Principal 106,00 Amount 112,36 for 2 years. 3d Principal 112,36 Amount 119,1016 for 3 yrs. Ans. .
2. What is the amount of 425 dollars, for 4 years, at 5 per cent. per annum, compound interest ?
Ans. $516, 59cts. 3. What will 400l. amount to, in 4 years, at 6 per cent. per annum, compound interest ? Ans. £504 195. 92d.
4. What is the compound interest of 1501. 10s. for 3 years, at 6 per ct. per annum? Ans. £28 14s. 111d. +
5. What is the compound interest of 500 dollars for 4 years, at 6 per cent. per annum ? Ans. $131,238+
6. What will 1000 dollars amount to in 4 years, at 7 per cent per annum, compound interest ?
Ans. 81310, 79cts. 6m. + 7. What is the amount of 750 dollars for 4 years, at 6 , per cent. per annum, compound interest ?
Ans. 8946, 85cts. 7,72m. 8. What is the canpound interest of 876 dols. 90 cm før 35 years, at 6 per cent. per annum ?
Ans. $198, 83cts.
DISCOUNT, an allowance inade for the payment of any sum of money before it becomes due; or upon advancing ready money for notes, bills, &c. which are payable at a future day. What remains after the discount is deducted, is the present worth, or such a sum as, if put to interest, would at the given rate and time, amount to the given sum or debt.
RULE. As the amount of 100?. or 100 dollars, at the given rate and time : is to the interest of 100, at the same rate and time : : so is the given sum : to the discount.
Subtract the discount from the given sum, and the remainder is the present worth.
Oras the amount of 100 : is to 100 : : so is the given sum or debt : to the present worth.
PROOF.—Find the amount of the present worth, at the given rate and time, and if the work is right, that will be equal to the given sum.
cent. a year?
1. What must be discounted for the ready payment of 100 dollars, due a year hence at 6 per $ $ $
100,00 given sum.
894,34 the present worth. 2. What sum in ready money will discharge a debt of 9251. due 1 year and 8 months hence, at 6 per
cent. ? £100
10 Interest for 20 months.
110 Am’t. £. £ £ k. s. d.
As 110 : 100 : 925 : 840 18 2+ Ans. 3. What is the present worth of 600 dollars, due 4 years hence, at 5 per cent. ?
Ans. $500 4. What is the discount of 2751. 10s. for 10 months, at 6 per cer
Ans. £13 28. 4 d.
5. Bought goods amounting to 615 dols. 75 cents, at 7 months credit ; how much ready money must I pay,
discount at 41 per cent. per annum ?
Ans. 8600. 6. What sum of ready money must be received for a bill of 900 dollars, due 73 days hence, discount at 6 per cent. per annum ?
Ans. 8889, 32cts. 8m. Note:- When sundry sums are to be paid at different times, find the Rebate or present worth of each particular payment separately, and when so found, add them into
EXAMPLES 7. What is the discount of 750l. the one half payable in six months, and the other half in six months after that, at 7 per cent. ?
Ans. £37 10s. 21d. 8. If a legacy is left me of 2000 dollars, of which 500 dols. are payable in 6 months, 800 dols. payable in 1 year, and the rest at the end of 3 years; how much ready money ought I to receive for said legacy, allowing 6 per cent. discount?
Ans. $1833, cts. 4m.
ANNUITIES. AN Annuity is a sum of money, payable every year, or
, for a certain number of years, or forever.
When the debtor keeps the annuity in his own hands, beyond the time of payment, it is said to be in arrears.
The sum of all 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 all at once at the beginning of the first year, the price which is paid for it is called the present worth. To find the amount of an annuity at simple interest.
RULE. 1. Find the interest of the given annuity for 1 year.
2. And then for 2, 3, &c. years, up to the given time, Jess 1.
3. Multiply the annuity hy the number of years given and add the product to the whole interest, and the sum will be the amount sought.