ato COMPOUND INTEREST, Is when the interest is added to the principal, at the end of ile year, and on that amount the interest cast for anoth. 1 er gear, and added again, and so on : this is called Inter est upon Interest. RULE. and add it to the principal, wliich call the amount for the first year; find the interest of tus 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 A the remainder will be the Compound Interest for the whole time. EXAMPLES 1. Required the amount of 100 dollars for 5 years Or per cent. per annum, compound interest INTEI $ cts. $ cts. PH Ist Principal 100,00 Amount 106,00 for 1 year. 2 Principal 106,00 Amount 112,36 for 2 years. tal 3d Principal 112,36 Amount 119,1016 for Ans: 2. What is the amount of 425 dollars, for 4 years, per cent. per annum, compound interest ? de Ans. 8516, 59cts. 5. What will 4001. amount to, in 4 years, at 6 per cente pey annum, compound interest : Ans. 6504 198. 9d. 4. What is the contpound interest of 1501. 10s. for 3 years, at 6 per ct. per annum ? Ans. 428 14s. 114d. + 3. What is the compound interest of 500 dollars for 4 years, at 6 per cent. per annum: Ans. 8131,258+ 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. 8946, 85cts. 7,72m. per annum : 4. at 5 for 3 years, per cent. 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 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. 0-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? $ cts. 100,00 given sum. 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 henee, at 6 per cent. ? £100 10 Interest for 20 months. £ s. d. 110 Am't. £ £ £. As 110 : 100 :: 925 · 840 18 2 + Ans, 3. What is the present worth of 600 dollars, due 4 fears hence, at 5 per cent, ? Ans. $500 4. What is the discount of 275l. 10s. for 10 months, at 6 per cent. per anoum- Ans. £18 2s. 4d. 5. Bought goods amounting to 615 dols. 75 cents, at7 months credit ; how much ready money Inust I pay, dis, count at 45 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. 6889, S2cts. 8m. Nore. 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 one sum, EXAMPLES. 7. What is the discount of 7501. 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 lols. 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. liscount? Aris. $1833, 37cts. 4m. ANNUITIES. AN Annuity is a sum of money, payable every year, or For a certain number of ycars, or forever. When the debtor keeps the annuity in his own hands, eyond the time of payment, it is said to be in arrears. The sum of all the annuities for thektime they have been yrborne, together with the interest due on each, is called he amount. 1 If an annuity is bought off, or paid all at once at the called the present worth. RULE. Ss 1, years given EXAMPLES 1. It an annuity of 701. be forborne 5 years, what will ke due for the principal and interest at the end of said term, simple interest being computed at 5 per cent. per annum? Yr. f. s. ist. Interest of 701. at 5 per cent. før 1- 3 10 27 0 -10 10 4-14 0 Zd. And 5 yrs, annuity, at 701. per yr. is 350 0 Ans. £$85 0 2. A house being let upon a lease of 7 years, at 400 dollars per annum, and the rent being in arrear for the whole termn, I demand the sum due at the end of the term, simple interest being allowed at 6l. per cent. per annun: Ans. $3304 To find the present worth of an annuity at simple interest. RULE. Find the present worth of each 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 ? 106 377,35849 Pres. worth of 1st yr. 112 357,14285 118 ; 100 :: 400 : 338,98305 124 322,58064 = ad yr. sd yr. 4th yr. Ans. $1396,06503 =$1396, 6cts. 51. 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, 57cts. 1m, 3. What is 80l. yearly rent, to continue 5 years, worth in ready money, at 6l. per cent. Ans. £340 15s of EQUATION OF PAYMENTS, Is finding the equated time to pay at once, several debts due at different periods of time, so that no loss shall be sustained by either party. RULE. Multiply each payment by its time, and divide the sum of the several products by the whole debt, and the quotient will be the equated time for the payment of the whole. EXAMPLES. 1. A owes B 380 dollars, to be paid as follows-viz. 100 olars in 6 months, 120 dollars in 7 months, and 160 duilars iu 10 months : What is the equated time for the payment of the whole debt. ? 100 X 6 = 600 120 X 7 840 160 x 10 = 1600 380 -)3040(8 months. Ans. 2. A merchant hath owing him 300l. to be paid as follows : 501. at 2 months, 1001. at 5 months, and the rest at 3 months; and it is agreed to make one payment of the whole ; I demand the equated time? Ans. 6 2.onths. 9. F owes H 1000 dollars, whereof 200 dollars is to be paid present, 400 dollars at 5, months, and the rest at 15 months, but they agree to make one payment of the whole; demand when that time must be? Ans. 8 months. 4. A merchant bas due to him a certain sum of money, be paid one sixth at 2 months, one third at 3 months, nd the rest at 6 months ; what is the equated' time for ne payment of the whole ? Ars. 4 months. BARTER, the exchanging of one commodity for another, and di-cts merchants and traders how to make the exchange thout loss to either party. RULE. Find the value of the commodity whose quantity is en; then find what quantity of the other at the pro be 1 |