TRUE DISCOUNT is the abatement on notes not yet due, or the difference between the sum of money at a certain rate, whose amount will be equal to the face of the note when due. Thus, a note for $100 due in one year without interest when money is worth 6%, is such a sum as will amount to $100 in one year. As $100 now is worth $106 at the end of the year, the present worth of money due in one year is 188 of the money due in one year. $112 at the end of two years is worth $100 now. $118 at the end of three years is worth $100 now, etc. COR.-The ratio for discounting is a diminishing ratio having 100 for the numerator, and the denominator is 100 increased by the interest for the time and rate. EXAMPLES. 1. What is the present worth of a note due in 1 year for $324, money worth 6%? 324 x 188 $305.66 + = 2. What is the present worth of a note due in 24 years for $675 at 5% ? Ans. $600. 3. What is the present worth of a note due in 4 years for $960 at 5%? Ans. $600. 4. What is the present worth of a note due in 15 months for $445 at 9%? Ans. $400. 5. What is the present worth of a note due in 9 months for $721 at 4%? Ans. $700. 6. What is the present worth of a note due in 13 months for $678 at 12% ? Ans. $600. EXCHANGE. Exchange is the system by which payments are made at a distant place by means of Bills of Exchange or Drafts. In a Bill of Exchange or draft, the person giving it or signing it is called the Drawer or Maker; the one to whom it is addressed is the Drawee, and the person to whom it is ordered to be paid is the Payee. The person in possession of the draft is the Holder, and if he sells it he must endorse it, which makes him responsible for the payment, unless otherwise specified. Exchange between the different cities of our own country is Domestic, and that with a foreign country is called Foreign Exchange. Exchange may be direct or circuitous; the latter is sometimes found to be advantageous. DOMESTIC EXCHANGE. PROBLEM. To find the cost of a draft on Philadelphia or New York, or any distant city, when at a premium and when at a discount; thus, if the premium is 1%, the draft will cost 18 of its face, which is the sum to be paid; when at a discount of 1%, it will cost of its face. EXAMPLES. 1. What is the cost of a draft on Philadelphia for $3024, at 1% premium? 15.12 1001 3024 × 100 = 180 = $3039.12. 2. What is the cost of a draft on New Orleans for $5000, at 1% discount? = 1% of $5000 $25. 3. What will this draft cost if drawn at thirty days, interest at 6%? 3 days grace must be allowed. = = H + 1 = rate per cent; The interest and discount must be reckoned on the face. $5000 $52.50 $4947.50. 4. My agent had in his possession $3288.60, which I directed him to remit; the draft received was $3240; what was the rate of exchange? 3288.60 3240.00 $48.60 = paid for a draft of $3240. 11 The rate is reduce by 32.4 = 48.60 3240.00' result will be the same if reduced to a decimal; thus, = 11%; the 100 10% = 100) 1.5000 (.015 1.5 REM. The ratio of the face of the draft and the premium paid on it, reduced to a fraction whose denominator is 100, will be the rate per cent of the draft; the same result is obtained by reducing the fraction to a decimal. The premium is the numerator, and the amount on the face of the draft the denominator of the fraction. 5. What is the cost of a 60 day draft on New York for $5480, at 1% premium, interest off at 6%? 6. What is the face of a draft which cost $1007.50, at % premium ? 7. What is the face of a draft that cost $992.50, at 4% discount? 8. What is the face of a draft on which $5 premium is paid, and the rate 1%? To = $5; 188 = $500, Ans. FOREIGN EXCHANGE, EXAMPLES. 1. What is the cost in New York of a draft on London for £546 15s. 6d., at 8% premium? 12) 6d. 20) 15.5 775 15s. 6d. 12 188 = j = .775. 24 3 109.355 8 2% £$46.775 × 3 × 188 = 109.355 × 8 × 3 = $2624.52. 100 25 5 12 546321871 × 30 × 108 = $2624.52. 40 2. What amount of debt in London may be paid by depositing $5000 in New York, rate of exchange 8% in favor of London ? 125 25 5000 × × 1 = 125 × 25 100 12 3 = £1041 13s. 4d. 3. What is the cost of a draft on London for £546.775 in New York, exchange $4.88 to the £ ? 546.775 × 4.88 = $2668.262. 4. What will a draft on London for £1041 13s. 4d. cost in New York, exchange $4.80 to the £? |