EXAMPLES. 1. What is the interest of 21. 5s. for a year, at 6 per ct.? £2 5s-45s. Interest 45 cts. the Answer. 2. Required the interest of 1007. for a year, at 6 per ct.? £100-2000s. Interest 2000 cts. $20 Ans. 3. Of 27s. 6d. for a year? Ans. 27s. is 27 cts. and 6d. is 5 m. 4. Required the interest of 5. 10s. 11d. £5 10s.=110s. Interest 110 cts. for a year? = 11 pence.-2 per rule leaves 9= VI. To compute the interest on any note or obligation, when there are payments in part, or endorsements. RULE.-1. Find the amount of the whole principal for the whole time. 2. Cast the interest on the several payments, from the time they were paid, to the time of settlement, and find their amount; and lastly, deduct the amount of the several payments from the amount of the principal. EXAMPLES. Suppose a bond or note dated April 17, 1793, was given for 675 dollars, interest at 6 per cent. and there were pay→ ments endorsed upon it as follows, viz. First payment, 148 dollars, May 7, 1794. Third payment, 99 dols. Jan. 2, 1798. I demand how much remains due on said note, the 17th June, 1798? cts. 148, 00 first payment, May 7, 1794. Yr. mo. 36, 50 interest up to-June 17, 1798.=4 11 184, 50 amount 341, 00 second payment, Aug. 17, 1796. Yr. mo. 378, 51 amount. 10 [Carried over. cts. 99, 00 third payment, January 2, 1798. $219, 52 remains due on the note, June 17, 1798. 2. On the 16th 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 16th of July, 1797 1st of Sept. 1798 $ 50 400 60 How stands the balance between us, on the 16th Novem ber, 1800? £62 10s. Ans. due to me, $63, 18 cts. 3. A PROMISSORY NOTE, viz. New-London, April 4, 1797. On demand, I promise to pay Timothy Careful, sixty-two pounds, ten shillings, and interest at 6 per cent. per annum, till paid; value received. JOHN STANBY, PETER PAYWELL. And payment June 4, 1800, 12 10 How much remains due on said note, the 4th day of De canber, 1800. £. s. d. Ans. 9 12 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 ous. 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 following EXAMPLE. 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 on his note. At the end of 10 years B takes up his note, and the sum he has to pay is reckoned 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 nine 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 interest, (as any one can see by casting it) is $70, 20 cts. this subtracted from 160 dols. the amount of the debt, leaves in favour of the creditor, $89, 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 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 dols. which he lent him. See a better Rule in Simple Interest by decimals. page 175: Σ COMPOUND INTEREST, IS when the interest is added to the principal, at the end of the year, and on that amont 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. EXAMPLES. 1. Required the amount of 100 dollars for 3 years at 6 per cent. per annum, compound interest? $cts. $ 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, 59 cts. 3. What will 4007. amount to, in four years, at 6 per cent. per annum, compound interest? Ans. £504 19s. 9&d. 4. What is the compound interest of 150l. 10s. for 3 years, at 6 per cent. 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. $1310, 79 cts. 6 m. + 7. What is the amount of 750 dollars for 4 years, at 6 per cent. per annum, compound interest? Ans. $946, 85 cts. 7,72 m. 8. What is the compound interest of 876 dols. 90 cents for 8 years, at 6 per cent. per annum? Aps. $198, 83 cts. DISCOUNT, IS an allowance made 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 1001. 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 tho present worth. Or as 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. EXAMPLES. 1. What must be discounted for the ready payment of 100 dollars, due a year hence at 6 per cent. a year? $3 As 1066: $ $cts. 100: 5 66 the answer. 100,00 given sum. 5,66 discount. $94,34 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. £. £. £. £. 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 275l. 10s. for 10 months, at Ans. £13 2s. 4d. 6 per cent. per annum? |