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 erroneous. 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, coinpletely expunge, or as it may be said qat up the debt. For an explanation of this, take the following EXAMPLE. A lends B 100 dollars, at 6 per cent. înterest, and takes his note of hand; B does no more than pay A at erery 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 dollais ; there are nine endorsements of 6 dollars each, upon which the debtor elains 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 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, 889, 40 cts. yr $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 dollars which he lent him. See a better Rule in Simple Interest by 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 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. 8 cts. 1st Principal 100,00 Amount 108,00 for 1 year. 1 2d Principal 106,00 Amount 112,36 for 2 years. 3d Principal 112,36 Amount 119,1016 for 3 YFS. Ans. 2. What is the amount of 425 dollars, for 4 years, at 5 per cent. per annum, compound interest ? Ans. 8516, 59cts. 3. What will 4001. amount to, in 4 years, at 6 per cent. per annum, compound interest: Ans. £504 195. 9 d. 4. What is the compound interest of 1501. 108. for 3 years, at 6 per ct. per annum ? Ans. 128 145. 11!d.+ 5. What is the compound interest of 500 dollars for 4 years, at 6 per cent. per annum ? Ans. 8131,2387 6. What will 1000 dollars amount to in 4 years, at 7 per cent per annum, compound interest ? Ans. $1310, 79cts. 6m. + 7. What is the amount of 750 dollars for 4 years, at 6 per cent. per annum, compound interest ? Ans. $946, 85cts. 7,72m. 8. What is the compound interest of 876 dols. 90 cts. for 39 years, at 6 per cent. per annum ? Ans. $198, 836to. + Is an DISCOUNT, allowance made for the payment of any sum of money before it becomes due; or upon arivancing ready money for notes, bills, &c. which are payable at a future day. What renrains 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 delt. RULE. As the amount of 1001. or 100 dollars, at the given rate "arid 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. Ormas tlie amount of 100 : is to 100 : : so is the given sum or debt: to the present worth. Proor. Find the annount 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, duc a year hence at 6 per cent. a year ? $ 8 8 cts. 100,00 given sam. 5,66 discount. $94,34 the present worth. 2. What sum in ready money will discharge a debt of 925l. due 1 year and 8 months hence, at 6 per cent. ? £100 10 Interest for 20 months. 110 Am't. £s £ f. S. d. As 110 : 100: ; 925 : 840 18 2-t Ans. 3. What is the preserit worth of 600 dollars, due 4 years hence, at 5 per cent. i Ans. $500 4. What is the discount of 2751. 10s. for 10 months, at 6 per cent. per annum ? ins. 613 25. 410 5. Bougl.t goods amounting to 615 dols. 75 cents, at 7 months credit; how much ready money must I pay, dis: count at 41 per cent. per annum ? Ans. $600. 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 ene sum. EXAMPLES 7. What is the discount of 7566. the one half payable in six months, and the other half in six-months after that, at 7 per cent. ? Ans. £37 10s. 2d. 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 resi at the end of 3 years; how much ready money ought I to receive for said legacy, allowing 6 per cent. discount? Ans. $1833, 37cts. 4in. ANNUITIES. AN Annuity is a sum of money, payable every year, or for a certain number of years, or forever. When the debtor keeps the annuity in his own hands, beyond the time of payment, it is said to be in arrcars. The sum of all the annuities for the time they have been forborne, together with the interest due on each, is called the amount. If an annuity is bought off, or paid all at once at the beginning of the first year, the price which is paid for it is called the present worth. To find the amount of an annuity at simple interest. RULE. 1. Find the interest of the given annuity for 1 year. 2. And then for 2, 3, &c. years, up to the given time, less 1. 3. Multiply the annuity by the number of years given and add the 'prorluct to the whole mterest, and the sum will be the amount sought. EXAMPLES. 1. If an annuity of 701. be forborne 5 years, what will 5 be due for the principal and interest at the end of said term, simple interest being computed at 5 per cent per annum? Ir. £$. Ist. Interest of 701. at 5 per cent. for 1- 3 10 2-7 0 3-10 10 4-14 0 2.1. And 5 yrs. annuity, at 701. per yr. is 350 0 Ans. £385 0 2. A house being let upon a lease of 7 years, at 400 dollars per annum, and the rent being in arrcar for the whole term, I demand the sum due at the end of the term. simple interest being allowed at 6l. per cent. per annum: Ans. $3504. To find the present worth of an annuity at simple interest. RULE. Find the present worth of cach year by itself, discount. ing from the time it falls due, and the sum of all these present, worths will be the present worth required. EXAMPLES. 1. What is the present worth of 400 dols. per annum, to continue 4 years, at 6 per cent. per annum? 6 1067 377,35849 Pres: worth of 1st yr. 112 : 100 :: 400 : . 357,14285 = 118 338,98305 3d yr. 124 322,58064 2d yr: 4th yr. Ans. 81396,06503=81396, Octs. 5m. 2. How much present money is equivalent to an annuity of 100 dollars, to continue 3 years ; rebate being made at 6 per cent. ? Ans. $268, 37cts. Im. 3. What is 80l. yearly rent, to continue 5 years, worth in ready money, at 6l. per cent.? Ans. £SÃO 15s. + |