RULE. Divide the given sum by the amount of $ 1 for the given rate and time, and the quotient will be the present worth. Or, multiply the given sum by 100, and divide the product by the amount of $ 100 for the given rate and time, and the quotient is the present worth. 2. What is the present worth of $ 152.64, due one year hence ? Ans. $ 144.00. 3. What is the present worth of $ 477.71, due four years hence ? Ans. $ 385.25. 4. What is the present worth of $ 172.86, due 3 years 4 months hence ? Ans. $ 144.05. 5. What is the present worth of $800, due 3 years 7 months and 18 days hence ? Ans. $ 656.81+. 6. Samuel Heath has given his note for $ 375.75, dated Oct. 4, 1842, payable to John Smith, or order, Jan. 1, 1844; what is the real value of the note at the time given ? Ans. $ 349.69+. 7. Bought a chaise and harness, of Isaac Morse, for $ 125.75, for which I gave him my note, dated Oct. 5, 1842, to be paid in six months ; what is the present value of the note Jan. 1, 1843 ? Ans. $ 123.81+ 8. My tailor informs me, it will take 10 square yards of cloth to make me a full suit of clothes. The cloth I am about to purchase is 14 yards wide, and on spunging it will shrink 5 per cent. in width and length. How many yards of the above cloth must I purchase for my " new suit" ? Ans. Gyd. Iqr. 1732 na. Section 40. COMPOUND INTEREST. The law specifies, that the borrower of money shall pay a certain number of dollars, called per cent., for the use of $ 100 for a year. Now, if this borrower does not pay to the lender this per cent. at the end of the year, it is no more than just, that he should pay interest for the use of it, so long as he shall keep it in his possession ; this is called Compound Interest. 1. What is the compound interest of $500 for 3 years ? Ans. $ 95.50. $500= Principal. 1.06 year. 500. 530.00 = Amount for 1 year. 1.06 years. years. 500 $95.50 = Compound interest for 3 years. From the above process, we see the propriety of the following RULE. Find the interest of the given sum for one year, and add it to the principal ; then find the interest of this amount for the next year; and so continue, until the time of settlement. Subtract the principal from the last amount, and the remainder is the compound interest. 2. What is the compound interest of $ 761.75 for 4 years ? Ans. $ 199.94, 3. What is the amount of $ 67.25 for 3 years, at compound interest ? Ans. $ 80.09+. 4. What is the amount of $ 78.69 for 5 years at 7 per cent. ? Ans. $ 110.33. 5. What is the amount of $ 128 for 3 years 5 months and 18 days, at compound interest ? Ans. $ 156 70. 6. What is the compound interest of $ 76.18 for 2 years 8 months 9 days? Ans. $ 12.96. II. To find the amount of a note at compound interest, when there have been partial payments. RULE. Find the amount of the principal, and from it subtract the amount of the indorsements. $ 144. Haverhill, Sept. 25, 1839. For value received, I promise to pay Charles Northend, or order, on demand, one hundred forty-four dollars, with interest. John Small, Jr. Attest, Q. Jones. On this note are the following indorsements. Jan. 1, 1840. Received thirty dollars. June 30, 1841. Received eighty dollars. Feb. 7, 1842. Received ten dollars. What is due on the above note at compound interest, 1842 ? Ans. $ 40.02. Oct. 4, OPERATION BY COMPOUND INTEREST. Principal $ 144.00 Interest from Sept. 25, 1839, to Oct. 4, 1842 27.76 Amount 171.76 First payment $ 30.00 Interest from Jan. 1, 1840, to Oct. 4, 1842 5.23 Second payment 80.00 Interest from June 30, 1841, to Oct. 4, 1842 6.12 Third payment 10.00 Interest from Feb. 7, 1842, to Oct. 4, 1842 39 Amount $ 131.74 Remains due, Oct. 4, 1842 $ 40.02 Section 41. EQUATION OF PAYMENTS. OPERATION. When several sums of money, to be paid at different times, are reduced to a mean time for the payment of the whole, without gain or loss to the debtor or creditor, it is called Equation of Payments. 1. John Jones owes Samuel Gray $ 100; $ 20 of which is to be paid in 2 months ; $ 40 in 6 months ; $ 30 in 8 months; and $ 10 in 12 months ; what is the equated time for the payment of the whole sum ? Ans. 6mo. 12da. By analysis, $20 for 2 $20 x 2 40 months is the same, as $40 X 6 = 240 $ 40 for 1 month ; and $30 x 8 = 240 $ 40 for 6 months is the $10 x12=120 same, $1 for 240 $100 100)6 4 0 ( 6 mo. months ; and $ 30 for 8 600 months is the same, $1 for 240 months ; and 40 $ 10 for 12 months is the 30 same, $ 1 for 120 100)1200(1 2 da. months; therefore, $1 1200 for 40 +240 +240 + 120 = 640 months is the same, as $ 20 for 2 months, $ 40 for 6 months, $ 30 for 8 months, and $ 10 for 12 months ; but $ 20 + $ 40+ $30 + $ 10 are $ 100 ; therefore, $1 for 640 months is the same, as $ 100 for ido of 640 months, which is 6 months and 12 days, as before. Hence the following as as as RULE. Multiply each payment by the time at which it is due, then divide the sum of the products by the sum of the pay. ments, and the quotient will be the true time required. 2. John Smith owes a merchant, in Boston, $ 1000, $ 250 of which is to be paid in 4 months, $ 350 in 8 months, and the remainder in 12 months ; what is the equated time for the payment of the whole sum? Ans. 8mo. 18da. Note. The following, example will illustrate the method, the merchants practise to find the medium time of payment of goods sold on credit. 3. Purchased of James Brown, at sundry times, and on various terms of credit, as by the statement annexed. When is the medium time of payment ? Jan. 1, a bill amounting to $ 360, on 3 months' credit. Jan. 15, do. do. 186, on 4 months' credit. March 1, do. do. 450, on 4 months' credit. May 15, do. do. 360, on 3 months' credit. June 20, do. do. 500, on 5 months' credit. FORM OF STATEMENT. Due April 1, $360 May 15, $186 x 45= 8370 )206 620(115215 days. 80 The medium time of payment will be 116 days from April 1, which will be July 25. 4. Sold S. Dana several parcels of goods, at sundry times, and on various terms of credit, as by the following statement. Jan. 7, 1841, a bill amounting to $375.60, on 4 months. Apr. 18, 1841, do. do. 687.25, on 4 months. June 7, 1841, do. do. 568.50, on 6 months. Sept. 25, 1841, do. do. 300.00, on 6 months. Nov. 5, 1941, do. do. 675.75, on 9 months. Dec. 1, 1841, do. do. 100.00, on 3 months. What is the equated time for payment of all the bills ? Ans. Dec. 24. |