CASE I. 639. To find the Average Time of Credit, or Equated Time of Payment, when the terms begin at the same time. 1. A owes B $300 due in 3, months, $400 due in 5 months, and $600 due in 6 months. What is the average time of credit if the whole account be paid at once ? PRODUCT METHOD. PROCESS. $1300× (5)=$6500×1 $6500 $1300-5 SOLUTION. The use or interest of $300 for 3 months is equivalent to the use or interest of 3 times $300-$900 for 1 month; the use of $400 for 5 months is equivalent to the use of 5 times $400-$2000 for 1 month; and the use of $600 for 6 months is equivalent to the use of 6 times $600=$3600 for INTEREST METHOD. 640. PROCESS. Interest of $300 for 3 mos. at 6% $ 4.50 Interest of $400 for 5 mos. at 6% 10.00 18.00 Int. of $1300 for (5) mos. at 6%=$32.50 Int. of $1300 for 1 mo. at 6% $ 6.50. $32.50÷$6.50-5. SOLUTION. Reckoning interest at 6%, the interest of $300 for 3 months is $4.50; the interest of $400 for 5 months is $10; the interest of $600 for 6 months is $18.00; and the interest of the several items for their respective terms of credit is $4.50+$10+$18=$32.50. The NOTE. Any rate of interest may be assumed with the same result. 641. I. Multiply each debt by its term of credit and divide the sum of the products by the sum of the debts: the quotient is the average term of credit. Or, II. Compute the interest of each debt for its term of credit, and divide the sum of the interests by the interest of the sum of the debts for one period of the same denomination as the several terms of credit: the quotient is the average time of credit. The average term of credit added to the date of the con traction of the debts if at the same date, or to the 2. On the 1st of January, 1892, a merchant owed for term of credit, and at what time may the whole debt 3. September, 1, 1891, my indebtedness was as follows: At 4. Bought a farm, Oct. 15, 1889, for $4800, paying down, in 9 months, and the balance in 1 year. At what time may the whole price be equitably paid? 5. A man purchased a house and lot for $5600; terms, $2000 cash, $1200 in 1 year, $1800 in 1 year and 8 months, and the balance in 2 years. For what time should a note be drawn to cover the purchase in a single payment? CASE II. 642. To find the Average Term of Credit, or Equated Time of Payment, when the Terms of Credit begin and mature at different times. 1. Find the equated time at which the following account may be settled: SOLUTION. Select, for convenience, the earliest date at which any item becomes due, July 5, as the focal date. $1250, the debt contracted May 5, is due on that day, and has no term of credit. $2460, the debt contracted June 10, is due Oct. 10, and has a term of credit of 97 days from the focal date. $1599, the debt contracted Aug. 1, is due Feb. 1, 1891, and has a term of credit of 211 days from the focal date. $2160, the debt contracted Sept. 15, is due Jan 15, 1891, and has a term of credit of 194 days from the focal date. In this manner the example becomes one in Case I. $1250 having no term of credit, its use or interest is equivalent to nothing; the use of $2460 for 97 days is equivalent to the use of 97 times $2460 $238620 for 1 day; the use of $1590 for 211 days is equivalent to the use of 211 times $1590=$335490 for 1 day; the use of $2160 for 194 days is equivalent to the use of 194 times $2160 $419040 for 1 day; and the use of the several debts for their respective terms of credit is equivalent to the use of $238620+ $335490+$419040=$993150 for 1 day, which is equivalent to the use of $7460, the sum of the debts, for as many days as $7460 is con tained times in $993150, which is 133+ times. July 5+133 days= Nov. 15, which is the equated time. 643. Select, for convenience, the earliest date at which any debt becomes due, as the focal date. From the focal date compute the term of credit for each item until its maturity, and proceed as in Case I. 2. Find the equated time for the following bill: 1892. Jan. 1. 36 yards of linen, @ $2.50 on 2 mo. Feb. 1. 40 yards of cambric, @ 60c., on 2 mo. Mar. 1. 60 yards of cloth, @ $8.00, on 3 mo. Apr. 1. 24 yards of velvet, @$16.00, on 3 mo., May 1. 50 yards of lace, @ $12.50, on 4 mo. 3. 1891, Jan. 20, A owes me $360; 4. Purchased the following goods on 6 months' credit: 5. A merchant bought goods as follows: 1892, Sept. 10, $500, on 6 mo.; Oct. 15, $440, on 2 mo.; Nov. 20, $560, on 3 mo.; and Dec. 25, $800, on 4 mo. At what time may the whole debt be equitably discharged? CHAPTER XIX. EQUATION OF ACCOUNTS. 644. An Account is a record of the items of debit and credit in business transactions. 645. A Merchandise Balance is the difference between the debits and credits of an account. 646. A Cash Balance is the merchandise balance plus or minus the interest thereon, according to the time of settlement. If settlement is made after the equated time, the cash balance is the balance of items plus the interest from the equated time to the time of settlement; but if settlement is made before the equated time, the cash balance is the balance of items minus the interest from the time of settlement to the equated time. 647. Averaging an Account is a method of finding the equated time for the payment of the balance of an account. CASE I. 648. To find the Equated Time for the payment of the Merchandise Balance of an account. 1. Dr. JAMES THOMPSON IN ACCT. WITH JOHN WILSON. Cr. Find the time when the balance of the account is due. |