2. Multiply twice the first payment by the ratio, and call this the second number. 3. Divide the first number by the second, and call the quotient the third number. 4. Call the square of the third number the fourth number. 5. Divide the product of the second payment and time between the payments by the product of the first payment and the ratio, and call the quotient the fifth number. 6. From the fourth number take the fifth, and call the square root of the difference the sixth number. 7. Then the difference of the third and sixth numbers is the equated time, after the first payment. EXAMPLE. There are 100D. payable in 2 years, and 106D. at 6 years hence; what is the equated time, allowing simple interest, at 6 per cent. per annum ? 1st. payment=100 Ratio='06 6.00 1st. payment 100 200 Time between the payments-4years. Mult. by the ratio='06 Add both payments={ 24 100 106 Div. by the 2d. num. 12)230=1st. number. 19.166+ 3d. number. 3d. number squared-367-335556-4th. number. Multiplied by the time= 4 12.00-2d. num. Sproduct of the 2d. payment and time between the payments. 1st. payment mult. by the ratio=6)424= 70.666+ 5th number. From the 4th. number=367.335556 Carried over. keeping of a fum of money after it is due, is evidently equal to the intereft of the debt for that time: And the lofs, which is fuftained by the paying of a fum of money before it is due, is evidently equal to the discount of the debt for that time: Therefore it is obvious that the debtor must retain the fum immediately due, or the first payment, till its intereft fhall be equal to the discount of the second fum for the time it is paid before due; because in that cafe the gain and lofs will be equal, and confequently neither party can be a loser. INSURANCE is a security, or assurance, by mean of a writ called a Policy, to indemnify the insured of such losses as shall be specified in the policy subscribed by the insurer, or insurers, by which the under writers oblige themselves to make good and effectual the property insured, in consideration of a certain premium at a stipulated rate per cent. (which varies according to the risk) to be immediately paid down, or otherwise secured according to the tenor of the agreement. The average loss is 10 per cent.; that is, if the insured suffer any damage or loss, not exceeding 10 per cent. he bears it himself, and the insurers are free. A policy should be taken out for a sum sufficient to cover the prin cipal and premium, and the business of this rule is, in general, to calculate what that sum should be. CASE I. When the premium, at a certain rate per cent. for insuring a sum, is required, the operation is the same as in interest, or commission. EXAMPLES. 1. What is the premium upon 5371. 15s. 9d. at 61 per cent. ? 1194 2. What is the premium upon D.375, at 7 per cent.? D.375 ⚫075 1875 2625 Ans. D.28 125 CASE II. To find the sum for which a policy should be taken out to cover a given sum. RULE. Take the premium from 1001. (or in federal money D.100 and say, As the remainder is to 100, so is the sum adventured to the policy. Or, In decimals, take the premium from 100, annex two cyphers to the sum to be covered, and divide by the remainder for the policy. EXAMPLES. 1. It is required to cover 7591. premium 8 per cent.: For what sum must the policy be taken? 2. A merchant sent a vessel and cargo to sea, valued at D.5760: What sum must the policy be taken out for, to cover this property, premium 19 per cent.? 100 Now it is plain, that if I want to recover 921. I must in this cafe, insure upon 1001.; therefore, to recover 7591. I must insure upon 8251.; for when 8 per cent. for premium is deducted, I shall have 7591. remaining nett. For £.825 fum insured upon at 8 per cent. 759 the first outset. In this and the following cafes, let x=100, p=premium, a amount to be in fired upon, and s=fum to be covered; then, x 100 D. D. D. c. 576000 Or, 80.5 == D.7155.28c.-Ans, as before. When a policy is taken out for a certain sum in order to cover a given sum. To find the premium, say, as the policy is to the covered sum; so is.100 (or D.100) to a fourth number, which, being taken from 100, will leave the premium.* Or, In decimals, divide the sum covered, with two cyphers annexed, by the policy; subtract the quotient from 100, the remainder is the premium. EXAMPLES. 1 If a policy be taken out for 12501. to cover 5001. What is the premium per cent.? 1250: 500 :: 100 Or, 100 2. If a policy be taken out for D.781-25, to cover D.625: Required the premium per cent. ? D. c. As 781-25 Or, 62500 781.25 625 :: 100: 87.50 And, 100—87.5-12·5, or 12 = 87.5, &c. as before. [per cent. premium, Ans. CASE IV. When the policy for covering any sum and the premium per cent. are given, to find the sum to be covered. RULE.-Deduct the premium per cent, from 100, and say, As 100 is to the remainder, so is the policy to the sum required to be covered. Or, In decimals, Multiply the policy by the remainder found as before, and point off two right hand places in the product for the answer. EXAMPLES. 1. If a policy be taken out for 12501. at 60 per cent.: What is the adventure, or sum to be covered ?+ 100 2. If a policy be taken out for D.781 25c. at 124 per cent. requir ed the sum covered? 781.25x100-12 As 100 100—121 :: 781·25 : =D.625, Ans. 100 Or, 781-25×100—12·5–62500; and 625·00, Ans. as before. CASE V. When a given sum is adventured several voyages round from one place to another, either at the same, or different risks, from place to place, and it is required to take out a policy for such a sum as will cover the adventure all round, supposing the risk out and home to be equal and tantamount to the several given risks. RULE. 1. Raise 1001. or D. to that power denoted by the number of risks, and multiply the said power by the sum adventured, (or to be covered for a dividend. 2 Subtract the several premiums, each, from 1001. and multiply the several remainders continually together for a divisor, and the quotient, arising from this division, will give the policy to cover the adventure the voyage round.* EXAMPLE. A merchant adventured D. 1500 from Boston to Philadelphia, at S per cent. from thence to Guadaloupe, at 4, from thence to Nantz, at 5, and from thence home at 6 per cent.: For what sum must he take out a policy to cover his adventure the voyage round, supposing the for as many voyages as may be required. Hence, making w➡exponent of any giv a m 3 -=sum to be insured upon, all round :—And x-xx-xx-p, &c. - the premium all round, tantamount to the several given prémiums; s, in this Theorem being equal to the firft adventure, and a-amount which will cover that adventure the voyage round. |