2. Divide the last product by the policy. 3. Extract that root of the quotient denoted by the number of risks. 4. Take this root from 100, and the remainder will be the equal premium from one port to the other. EXAMPLES. A merchant adventured $1500 from Boston to Philadelphia, thence to Guadaloupe, thence to Nantz, and thence home; to cover which all round he took out a policy for $1803-835; and the premium was equal from one place to the other: what was the premium per cent. ? 4 100 100×100×100 × 100 × 1500=4.507 per cent. Answer. CASE VIII. When an adventure is insured out and home at one risk, at a given rate per cent. and the voyage terminates short of what was at first intended: To find what the underwriter must receive per cent. RULE. 1. If just half the voyage is performed, it must be considered as two equal risks: If one third, then, as three equal risks; if but one fourth, then, as four risks, and so on; and by Case 2d must be found the amount which will cover the adventure the voyage round. 2. Involve 100 to that power denoted by the number of risks, and multiply this power by the sum adventured. 3. Divide this product by the aforesaid amount. 4. Extract that root of the quotient denoted by the number of risks. 5. Take this root from 100, and the remainder will be the sum per cent. which the underwriter must receive. EXAMPLE. A merchant covers $200 at 6 per cent. from Newburyport to the West Indies and home again; but the voyage terminating in the West Indies, what must the insurer receive per cent.? 100 6 94 100 200 212-765957=amount to cover $200 voyage round. 2000000 100x100×200=2000000 and ;=9400, and 100-√9400 212-765957 -3-0465 to be paid the insurer per cent. upon the above amount. ance raised to a power whose index is the number of years. If that root of the quotient, indicated by the number of years, be extracted, you will have the diffe rence between 100 and the rate per cent, and this difference taken from 100 gives the rate. COMPOUND INTEREST Is that which arises from the interest being added to the principal, and (continuing in the hands of the borrower) becoming part of the principal, at the end of each stated time of payment. METHOD I RULE.* Find the amount of the given principal, for the time of the first payment, by Simple Interest: next, find the interest of that sum, or principal, and add it as before, and thus proceed for any number of years, still accounting the last amount as the principal for the next payment. The given principal being subtracted from the last amount, the remainder will be the compound in terest. In federal money, multiply the principal by the rate for the first time of payment, setting the product two places more to the right than the multiplicand, and the decimal point in the product under that in the multiplicand; then find the amount, and proceed as above. Note. It is not usually necessary to carry the work beyond mills; therefore, when the figure next beyond mills, at the right, exceeds 5, increase the number of mills 1; when it does not exceed 5, it may be omitted. The result will be exact enough for common purposes. EXAMPLES. 1. What will £480 amount to in 5 years, at 6 per cent. per annum? £ Princioal for the 1st year 480 0 Interest of ditto 28 16 Principal 480 Rate of interest 6 * It may be observed that all the computations, relating to Compound Interest, are founded upon a series of terms, increasing in Geometrical Progression, wherein the number of years assigns the index of the last and highest term: Therefore, as one pound is to the amount of one pound, for any given time, so is any proposed principal, or sum to its amount for the same time. Amount for 5 years 642 6 11 Compound interest for 5 years 162 6 11 In federal money, thus: The principal being $1600 for five years, Principal for the 1st year $1600 Rate of interest 6 Interest 1st year 96.00 Amount 1st and prin. 2d year 1696 6 Carried over. Brought over. Interest 5th year 121-19778816 Amount for 5 years 2141-16092416 Compound Interest for 5 years Or thus: 1st principal $1600. 6 Interest 96.00 2d principal 1696· 6 541-16092416 $740 for 6 years, at 4 per Ans. $196 33c. 6m. years, at £4 per cent. per Ans. £486 13s. 2d. 4. What will £150 amount to in a year, at 2 per cent. per month? Ans. £190 4s. 5d. 5. What is the compound interest of $500 at 2 per cent a month Ans. $134 12c. 1m. for one year? 6. What is the amount of $100 at 6 per cent. compound interest for 3 years? 7. What is the compound interest of $100 at 7 per cent. for 3 years? METHOD II. When the rate is at 5 per cent. per annum. 1. Divide the principal by 20, and this quotient, added to the principal, will be the amount for the first year, and the principal for the second. 2. In like manner find the amount for every succeeding year. When the rate is at 6 per cent. per annum. 1. Divide the principal by 20, and that quotient by 5: these quotients, added to the principal, will be the amount for the first year, and the principal for the second. 2. In like manner obtain the amount for every succeeding year. EXAMPLES. 1. What is the amount of £480 2. Of the same sum at 5 per at 6 per cent. per annum, for 5 cent. per annum, for 5 years. years? 20)480 5) 24 4 16 £ 20)480 24 A Table of the Amount of £1 or $1, at per cent. per month, as practised at the Banks. |