OPERATION. Principal on interest from May 1, 1889 Amount. Payment Dec. 25, 1889 Remainder for a new principal. Interest from Dec. 25, 1889, to June 14, 1892, 2 yr. 5 mo. 19 da. Amount . Payment July 10, 1890, less than interest then due Their sum less than interest then due Payment June 14, 1892 Their sum exceeds the interest then due Remainder for a new principal Interest from June 14, 1892, to April 15, 1893, 10 mo. 1 da. $475.50 21.63 $497.13 50 $447.13 $15.75 25.50 77.29 $524.42 $41.25 104 $145.25 $379.17 22.19 $401.36+ These examples have been worked according to the method prescribed by the Supreme Court of the U. S., and are sufficient to illustrate the following rule: UNITED STATES RULE. I. Find the amount of the given principal to the time of the first payment, and if this payment equals or exceeds the interest then due, subtract it from the amount obtained, and treat the remainder as a new principal. II. But if the interest is greater than any payment, find the amount on the same principal to a time when the sum of the payments equals or exceeds the interest then due ; subtracting the sum of the payments from that amount, the remainder will form a new principal, on which interest is to be computed as before. $514.96. SAN FRANCISco, June 20, 1888. 3. Three years after date we promise to pay Ross & Wade, or order, five hundred fourteen and 96 dollars, for value received, with 10% interest. 100 WILDER & BRO. On this note were indorsed the following payments: Nov. 12, 1888, $105.50; March 20, 1890, $200; July 10, 1890, $75.60. How much remains due on the note at the time of its maturity? Ans. $242.12+. $3000. CHARLESTON, May 7, 1889. 4. For value received, I promise to pay George Babcock three thousand dollars, on demand, with 7% interest. JOHN MAY. On this note were indorsed the following payments: Sept. 10, 1889, received. Jan. 1, 1890, 66 Oct. 25, 1890, April 4, 1891, How much was due Feb. 20, 1892? Ans. $1344.35+. $912,75 NEW ORLEANS, Aug. 3, 1889. 100 5. One year after date I promise to pay George Bailey, or order, nine hundred twelve 5 dollars, with 5% interest, for value received. JAMES POWELL. 66 $25 500 75 1500 The note was not paid when due, but was settled Sept. 15, 1892, one payment of $250 having been made. Jan. 1, 1891, and another of $316.75, May 4, 1892. How much was due at the time of settlement? Ans. $467.53+. 312. The following method of computation is often used by merchants in the settlement of notes and of interest accounts running a year or less: MERCANTILE RULE. I. Find the amount of the principal from the date of the note to the time of settlement. II. Find the amount of each payment from the time it was made to the time of settlement. III. Subtract the sum of the amounts of the payments from the amount of the principal, and the remainder will be the sum due. An accurate application of this rule requires that exact interest be computed by the rule for days. (See page 273, Ex. 4.) 1. On a note for $600 at 7%, dated Feb. 15, 1893, were the following indorsements: March 25, 1893, $150; June 1, 1893, $75; Oct. 10, 1893, $100. What was due Dec. 31, 1893 ? OPERATION. Am't of $600 from Feb. 15 to Dec. 31, 319 da., 66 66 Mar. 25" "$150 66 66 66 June 1 " 213" Balance due Dec. 31, 1874, 66 281 66 $158.08 $636.71 78.06 101.57 337.71 $299.00 2. A note for $950, dated Jan. 25, 1892, payable in 9 mo., at 7% interest, had the following indorsements: March 2, 1892, $225; May 5, 1892, $174.19; June 29, 1892, $187.50; Aug. 1, 1892, $79.15. What was the balance due at the time of its maturity? Ans. $312.46. 3. Payments were made on a debt of $1750, dated April 5, 1891, as follows: May 10, 1891, $190; July 1, 1891, $230; Aug. 5, 1891, $645; Oct. 1, 1891, $372. What was due Dec. 31, 1891, interest at 6% ? Ans. $355.16. PROBLEMS IN INTEREST. 313. In all examples in interest there are five parts to be considered, the Principal, the Rate, the Time, the Interest, and the Amount. These parts bear such a relation to one another, that any three of them being given (provided one of the three be the time or rate), the other two may readily be found. Hence there are many problems in Simple Interest, but the five following cases are the ones that occur most frequently in business transactions. * I. The principal, rate, and time being given, to find the interest and amount. II. The time, rate, and interest being given, to find the principal and amount. III. The time, rate, and amount being given, to find the principal and interest. IV. The principal, time, and interest being given, to find the rate and amount. V. The principal, interest, and rate being given, to find the time and amount. EXAMPLES. 314. The time, rate per cent, and interest being given, to find the principal and amount. 1. What principal in 2 years, at 6%, will gain $ 31.80 interest, and what will be the amount? SOLUTION. Since $1, in 2 years, at 6%, will gain $.12 interest, the principal that will gain $31.80, at the same rate and time, must be as many dollars as $.12 is contained times in $31.80; dividing, we obtain $265, the required principal. Adding this principal to the interest, we obtain $298.80, the Amt. *This case has been explained in § 307. OPERATION. $.12, interest of $1 in 2 years, at 6 per cent. $31.80 ÷ $.12 $265, Prin. $265 +$31.80 $296.80, Amt. = RULE.-I. Divide the given interest by the interest of $1 for the given time and rate, and the quotient will be the principal. II. Add the principal and interest to obtain the amount. 2. What principal, at 6%, will gain $28.121 in 6 years 3 months? Ans. $75. 3. What sum, put at interest for 4 months 18 days, at 4%, will gain $9.20 ? Ans. $600. 4. What sum of money, invested at 7%, will pay me an annual income of $1260 ? Ans. $18000. 5. What sum must be invested in real estate, yielding 10% profit in rents, to produce an income of $3370 ? Ans. $33700. 315. The time, rate per cent, and amount being given, to find the principal and interest. 1. What principal in 2 years 6 months, at 7%, will amount to $88.125, and what will be the interest? OPERATION. $1.175 Amt. of $1 in 2 years 6 months at 7%. $88.125 - $75 $13.125, Int. SOLUTION. Since $1, in 2 years 6 months, at 7%, will amount to $1.175, the principal that will amount to $88.125, at the same rate and time, must be as many dollars as $1.175 is contained times in $88.125; dividing, we obtain $75, the required principal. Subtracting this principal from the amount, we obtain the interest. = RULE. I. Divide the given amount by the amount of $1 for the given time and rate, and the quotient will be the principal required. II. Subtract the principal from the amount to obtain the interest. |