EXAMPLES. 1. What is the premium of insuring 8250 dollars, at 6 per cent. ? 8250 6 495,00 Ans. 495 dollars. 2. What is the premium of insuring 1650 dollars, at 151 per cent. ? Ans. 255dolls. 75cts. 3. What sum must be received for a policy of 1653 dollars, deducting a premium of 23 per cent.' for insurance ? Ans. 1276dolls. 66cts. 4. What is the premium for the insurance of 4000 dollars, at 75 per cent. ? Ans. 305 dollars. 5. What sum must be insured upon to cover 1800 dollars, when the premium is 10 per cent. ? 100 Policy. Deduct 10 Premium. 90 Sum covered. $1800 : $2000 Ans. DISCOUNT. Discount is an allowance made for the payment of any sum of money before it becomes due ; and is the difference between that sum due some time hence, and its present worth. The present worth of any sum, due some time hence, is such a sum, as, if put to interest, would in that time, and at the raie per cent. for which the discount is to be made, amount to the sum or debt then due. RULE.--As the amount of 100 dollars for the given rate and time, is to the interest of 100 dollars for that time, so is the given sum or debt, to the discount required. as the amount of 100 dollars or pounds, is to 100, so is the given sum or debt, to the present worth required. Note.—When goods are bought or sold, money advanced, bank-bills exchanged, &c. and discount is to be Or, made at any rate per cent. without time, the interest of the sums as found for a year, is the discount. EXAMPLES 1. What is the discount of 1912 dollars, 50 cents due 3 years hence, at 41 per cent. ? 4,50 3 13,50 cts. $. cts. $113,50 : 13,50 : : 1912,50 : 227,47 +Ans. 2. What is the present worth of 760 dollars due in 8 months, discount at 6 per cent. per annum ? %. 8. 100 760 : Ans. 730dolls. 76cts. 9mills. + 3. what is the present worth of 500 dollars payable in of a year, discount being at 5 per cent. ? Ans. $493,82 cts. + Note.-When several sums are to be paid at various times, find the discount or present worth of each sum separately, and then add those discounts of present worths into one sum, in order to obtain the required answer. 4. A is to pay 592 dollars, 70 cents on the first day of April, 1833, and 598 dollars, 90 cents the first of July following. It is required to know how much money will discharge both sums on the first of January, 1833, discounting at 8 per cent. per annum. Ans. 1156dolls. 94cts. 3mills. + 5. Bought a quantity of goods for 500 dollars ready money, and sold them again for 666 dollars, 67 cents, payable at ij of a year; what was the gain in ready money, supposing discount to be made at 5 per cent. ? Ans. 142dolls. 57cts. + 6. How much ready money will discharge a note for 150 dollars due in 60 days, allowing 6 per cent. per annum discount? Ans. 148dolls. 51cts. 4mills. + 7. If a legacy of 2000 dollars be left to me; 500 dollars payable in 6 months ; 800 in one year; and the rest at the end of 3 years; and the executor be willing to make me present payment, discounting at 6 per cent. ; what ought I to receive ? Ans. 133:3dolls. 37cts. 4m. + 8. What is the present worth of £60, payable at 3 and 6 months, at 5 per cent. per annum discount ? Ans. 258 17s. 11d. 23.gqr. ANNUITIES. AN ANNUITY is a yearly income arising from money, &c. and is either paid for a term of years, or upon a life. Annuities or pensions are said to be in arrears, when they are payable or due either yearly, balf-yearly, or quarterly, and yet remain unpaid for any number of payments. The sum of all the annuities, for the time they have been forborne, together with the interest due upon each, is called the amount. If an annuity be 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. CASE I. To find the amount of an annuity at Simple Interest. Rule.-1. Find the interest of the given annuity for 1 year; and then for 2, 3, &c. years, up to the given time less 1. 2. Multiply the annuity by the number of years given, and add the product to the whole interest, and the sum will be the amount required. EXAMPLES. 1. If 250 dollars, yearly annuity, be forborne 7 years, what will it amount to in that time, allowing simple interest at 6 per cent. per annum ? 1st. Interest of $250, at 6 per cent. for 1 year =$15. 2yrs.=$30. 3yrs.= $45. 4yrs.= $60. 5yrs.=$75, and 6yrs.=$90. And 2d. $250x7=$1750.. Then, 15+30+45+60+75+90+1750-$2065 Ans. 2. A house is leased for 7 years, at 400 dollars per annum; and the rent is unpaid during the whole term; wbat sum is due at the end of the lease, simple interest being allowed, at 6 per cent. per annum ? Ans. 3304 dollars. CASE II. To find the present worth of an annuity at Simple Interest. Rule.—Find the present worth of each year by itself, discounting from the time it falls due ; the sum of all these present worths, will be the present worth required. Note.-The divisions are continued decimally.-But it is deemed more equitable to allow compound interest, in purchasing annuities. . EXAMPLES. 1. What is the present worth of 400 dollars per annum, to continue 5 years, at 6 per cent. per annum ? 106 377,35819=present worth of 1 yr. 112 357,14285= 118 : 100 :: 400 : _ 339,98305= 124 322,58064 = 130 307,6923 2d yr. 3d yr. 4th yr. 5th yr. Ans. $1703,75733=$1703,75cts. 7m. 2. What is a salary of $300 per annum, to continue 5 years, worth, in ready money at 5 per cent. per ann. ? Ans. $1309,31cts. + 3. What is £250 yearly rent, to continue 6 years, worth in ready money, at 3 per cent. ! Ans. £1360 79. 103 d. + EQUATION OF PAYMENTS. EQUATION OF PAYMENTS is finding a time to pay at once several debts due at different times, so that no loss shall be sustained by either party, RULE.-Multiply each payment by the time at which it is due ; then divide the sum of the product by the sum of the payments, and the quotient will be the time required. EXAMPLES. 1. A owes B 1900 dollars, to be paid as follows, viz. 500 dollars in 6 months, 600 dollars in 7 months, and 800 dollars in 10 months; what is the equated time to pay the whole debt ? 500 x 6=3000 2. A owes B 240 dollars to be paid in six months; but in 11 months pays him 60 dollars, and in 44 months after that 80 dollars more ; how much longer than six months should A in equity defer the rest ? Ans. 2 months. 3. I owe 6512 dollars, to be paid in 3 months, 1 in 5 를 months, f in ten months, and the remainder in 14 months; at what time ought the whole to be paid ? Ans. 64 months. 4. A owes 60 dollars to be paid in 90 days, 75 dollars in 60 days, and 50 dollars in 30 days; what is the equated time for the whole to be paid ? Ans. 61 6days. + EXCHANGE. By this rule merchants know what sum of money ought to be received in one country, for a given sum of different specie paid in another, according to a given course of exchange. By the following table the moneys of foreign nations may be reduced to that of the United States. |