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675, 00 moto, dated April 17, 1733.
884, 25 amount of the note.
$219, 52 remains due on the note, June 17, 8798. 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, 1790 16th of July, 1797
400 1st of Sept. 1798 How stands the balance between lis, up the 16th Ny. yember, 1800 ?
Ans, due to me $6s, iScis. S. Å IROMISSORY VOTE, viz. 462 10s.
Veu-Londur, mil 4, 1797. On demand I promise to pay 'i'imothy Coreíul, sixtytwo pounds, ten shillings, anti interest at 6 per cent. per annum, till paid; value receive:i. JOHN STAXBY,
PETER PAYIVELI.. RICHARD TESTIS.
Indorsemenis. ist. Reccived in part of the above note, Scptember 4, 1709.
50 And payment June 4, 1900,
19 10 flow much remains due on said note, thus litrdi daya December, 1800 ?
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 stort periods of time, but in as long course of years it will be found to be very erroneous.
Althougla 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, conpletely expinge, or as it inay be said eat up the debt. For an explanation of this, take the following
A lends B 100 dollars, at 6 per cert. 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 on his note. At the end of 10 years B takes up his note, ane? the sum he has to pay is reckoned thus : The principal 100 dollars, on interest 10 years amounts to 160 dollais; there are nine endorsements of 6 dollars cach, upon which the debtor clains interest; one for 9 years, the second for 8 years, the tiird for years, aniso down to the time of settlement; the whole amount of the several endorsements and their interest, (as any one can see by casting ít) is $70, 20 cts. this subtracted from 100 dols. the amount of the debt leaves in favour of the creditor, 889, 40 cts. or $10,20 cts. less than the original principal, of which he has not received a cent, but only its annual interest.
If the same note shouil lic 20 years in the same way, B would owe but 57 dols. 60 cis. without paying the least fraction of the 100 dollars borrowed.
Extend it to 28 years, and A. the creditor would all in debt to B without receiving a cent of the 100 dollars which he lent him. Sco a better Rule in Simple Intercat by Decimals, page 175.
COMPOUND INTEREST, Is when the interest is added to the principal, at the end of the year, and on the 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 eccond, and so on for any number of years required. Subtract the original principal from the last ainoant, and the remainder will be the Compound Interest for the whole time.
EXAMPLES 1. Required the amount of 100 dollars for 3 years at 6 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 ycars. 3d Principal 112,36 Amount 119,1016 for 3 yrs. Ans.
2. What is the anount of 425 dollars, for 4 years, at 5 per cent. per annum, compound interest :
Ans. $516, 59c1s. S. What will 4001. amount to, in 4 years, at 6 per cent. per annum, compound interest: Ans: £504 198. 9jd. 4. What is the compound interest of 1501. 10s. for 3
Ans. 28 14s. 11 d. + 5. What is the compound interest of 500 dollars for 4 years, at 6 per cent. per annun: Ps. 8131,258.
6. What will 1000 dollars amount io in 4 years, at 7 per cent per annun, compound interast:
włns. $1310, 790's. Om. + ht. What is the amount of 750 dollars for 4 years, at 6 per cent. per annum, compound interest?
Ars. S946, S5cts. 7,7211. 8. What is the compound interest of 276 dols. 90 cts. for 32 years, at G per cert. peranpum?
ans. $198, 83cts.
years, at 6
DISCOUNT, Is an allowance made for the payment of any sum of money before it becomes due ; or upon advancing ready money for notes, bilis, &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 tiine, amount to the given sum or debt.
RULE. As the amount of 100l. 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 sim: to the discount.
Subtract the discount froin the given sum, and the remainder is the present srorth.
Or as the amount of 100 : is to 100 : : so is the given sum or debt: to the present worth.
Proor. Find the amount of the present worth, at the given rate and time, and if the wo:k is right, that will be equal to the given sum.
1. What must be discounted for the ready payment of 100 dollars, due a year hence at 6 per cent. a year :
'S S 8 $ cis.
100,00 given sum.
SI4,34 the present worth. 2. What sum in realy money will discharge a debt of 925l. due 1 year ani 8 months hence, at 6
per cent. :
10 Interest for 20 months.
110 An't. £ 6. $. £,. S. d.
As 110 : 100 :: 925 : 840 18 24 Ans. 3. What is the present worth of 600 dollars, due 4 gears hence, at 5 per cent. :
Ans. $500 4. What is the discount of 275l. 10s. for 10 inonths, at 6 per cent. per annum ? Ins. £IS 2s. 43
5. Bought gouis amounting to 615 dols. 75 cents, inty months creclit; how much ready money must I pay, discount at 41 per cent. per annum? Jis, 8600.
6. What sum of ready money must be received for it bill of 900 dollars, due 73 days hence, discount at 6 per cent. per annum ?
Ans. $889, Sects. 8m. Nore.When sundry suns are to be paid at different times, find the Rebate or present worth of cach particular payment separately, and when so found, add them into
6. Wind is the cliscount of 7561. the one half payable in six months, and the other half in six months after that, ül. 7 parceiiii
sins. £87 10s. 214. 8. If a legacy is left me of 2000 dollars, of which 500 tlols. are payable in 6 montis, 800 dols. payable in 1 year, and the rest at the end of 5 years; how much ready money ought I to receive for Emici legacy, allowing per cent. discount:
A128. $1833, S7cts. 41.
ANNUITIES.CA AN Annuity is a sum of mouey, payable every year, or for a certain number of years, or forever.
When the debtor keeps the annuity in his own hands, heyond 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 interestele on encl, is called the amount.
If an annuity is bought of or paid all at once at the beginning of the first year, the price wiich is paid for it is called the present worth. To find the amount of an annuity at simple interest.
RULE. i Find the interest of the given annuity for 1 year.
2. And then for 2, 3, &c. yers, up to the given time, less 1.
S. Multiply the annuity by the number of years given and add the product to the whole interest, and the sum will be the mount sought: