343. Most of the States have adopted the United States Rule for computing the amount due upon any obligation where partial payments are made, based upon the following principle. PRINCIPLE.-The indebtedness should be computed whenever a payment is made, but the principal must not be increased by the addition of interest. WRITTEN EXERCISES. 1. A note was given, Jan. 1, 1870, for $700. The following payments were indorsed upon it: May 6, 1870, $85; July 1, 1871, $40; Aug. 20, 1871, $100; Jan. 10, 1873, $350. How much was due Sept. 30, 1874, interest at 6%? Int. from May 6, 1870, to July 1, 1871,—1 yr. 1 mo. 25 da. Second payment, less than interest due Int. on $629.58 from July 1, 1871, to Aug. 20, 1871, Int. from Aug. 20, 1871, to Jan. 10, 1873,-1 yr. 4 mo. 24.08 $257.20 Int. from Jan. 10, 1873, to Sept. 30, 1874,-1 yr. 8 mo. 20 da. UNITED STATES RULE.-Find the amount of the principal to a time when a payment, or the sum of the payments, equals or exceeds the interest due, and from this amount subtract such payment or payments. With the remainder as a new principal, proceed as before. 2. A note for $2500, dated July 10, 1871, bore the following indorsements: Sept. 15, 1871, $150; Nov. 12, 1871, $300; Dec. 1, 1871, $100; April 3, 1872, $325; May 15, 1872, $275; Sept. 20, 1872, $1000. How much was due Jan. 1, 1873, the rate of interest being 6%? 3. How much was due at maturity on a note for $2150, dated Sept. 20, 1873, to run 2 years 6 months, on which the following payments were indorsed: Dec. 15, 1873, $75; Feb. 4, 1874, $200; April 3, 1874, $150; July 1, 1874, $500; Dec. 16, 1874, $1000, the rate of interest being 8%? 4. A note for $6725, dated Feb. 10, 1875, had the following indorsements: May 5, 1875, $275; Aug. 15, 1875, $50; Nov. 12, 1875, $1000; Jan. 3, 1876, $184.25; Sept. 13, 1876, $84.10; Dec. 23, 1876, $1000. How much was due Feb. 10, 1877, interest at 6%? 5. A bond was given April 4, 1870, for $5825, with interest at 8%. The following payments were indorsed upon it: May 15, 1871, $728.50; April 8, 1872, $1000; Dec. 12, 1872, $125; July 9, 1873, $980; June 12, 1874, $1000. much remained due upon the bond April 4, 1875? How 6. Sept. 25, 1872, James Hanna gave his note for $895.75 with interest at 10%. He paid on it as follows: Jan. 10, 1873, $25; Oct. 12, 1873, $200; Jan. 18, 1874, $75; March 25, 1874, $187.50; Jan. 1, 1875, $375. How much was due when he paid the note, Nov. 15, 1875? 7. Required, the balance due on a note dated Jan. 1, 1875, for $580 at 5%, to run 2 years, on which a payment of $85 was made every 3 months. 8. A note for $10000, with interest, dated Milwaukee, Wis., Dec. 12, 1875, was indorsed as follows: Feb. 23, 1876, $750; July 17, 1876, $108.25; Nov. 23, 1876, $3000; Jan. 18, 1877, $4000. How much was due May 12, 1877, interest at 8%? 9. Required, the balance due July 8, 1876, on a note for $3124.75, at 8% interest, dated Feb. 15, 1874, on which a payment was made Dec. 23, 1874, of $985; another of $875.35, Feb. 15, 1875; another of $1025, Feb. 20, 1876. 10. $1885.75. DETROIT, MICH., Feb. 10, 1874. Two years after date, for value received I promise to pay W. W. Heilbronner or order, One Thousand Eight Hundred Eighty-five 15 Dollars, with interest. 75 100 C. H. VIDRARD. On this note were the following indorsements: June 30, 1874, $50; Nov. 8, 1874, $100; Feb. 5, 1875, $125; April 17, 1875, $500; Dec. 1, 1875, $500. How much remained unpaid Mar. 1, 1876? PROBLEMS IN INTEREST. PROBLEM I. 344. Principal, rate, and time given, to find the interest. This has already been solved. (See page 220.) RULE.-Multiply the interest of $1, for the given rate and time, by the principal. PROBLEM II. 345. Principal, rate, and interest given, to find the time. 1. How much is the interest of $100 for a year at 6%? For 2 years? For 3 years? 2. When $100, loaned at 6%, brings an income of $12, for how long a time was it loaned? How long when the in terest was $18? $24? $3? $4? $2? $1.50? 3. When $50, loaned at 10%, brings an income of $10, for how long a time was it loaned? RULE.-Divide the given interest by the interest of the prin cipal for one year. In what time will 4. $250 produce $30 interest at 6%? 10. $150 double itself at 8% ? 11. Any sum double itself at 5%? 6%? 7%? 12. Any sum triple itself at 5%? 6%? 7%? PROBLEM III. 346. Principal, time, and interest given, to find the rate. 1. What is the interest of $100 for 1 year at 1%? At 2%? At 3%? 2. When the interest of $100 for 1 year was $8, what was the rate? 3. When the interest of $100 for 2 years was $14, what was the rate? 4. When the interest of $50 for 3 years was $15, what was the rate? RULE.-Divide the given interest, by the interest of the principal for the given time, at 1 per cent. What is the rate per cent. when the interest 5. Of $125 for 2 years is $15? 6. Of $250 for 6 months is $8.75? 7. Of $415 for 2 years 6 months is $56.025? 8. Of $317 for 1 year 5 months is $31.44? 9. Of $215 for 2 years 7 months 10 days is $39.30? PROBLEM IV. 347. Rate, time, and interest given, to find the principal. 1. At 6%, what sum will produce $6 yearly? 2. At 6%, what sum will produce $12 yearly? What $18 yearly? What $12 in two years? What $18 in 2 years? RULE.-Divide the given interest by the interest of $1, for the given time at the given rate. What sum of money will produce 3. $36.60 interest in 2 years at 6%? ? 4. $35.70 interest in 2 years 6 months at 8% |