10. If I am paid $37.26 as the interest due on money lent for 2 years and 17 days, at 7 %, what was the sum lent? Ans. $260.00. 11. What would be the difference between the interest of $10000 from July 1st to January 1st following, computed first by months, and then by days, counting 365 days to the year? Ans. $2.465+ more by the latter method. PRESENT WORTH.* 302. The Present Worth of a sum of money, payable at a future time without interest, is such a sum as, being placed at interest, at the given rate, will amount to the debt when it becomes due. The DISCOUNT is the interest on the present worth, deducted or abated from the apparent value of the debt, for present payment. It is the difference between the real and apparent value of the debt, and, for distinction, is called true discount. 303. To find the present worth of any sum. 1. Find the present worth of $480, due in 4 years, without interest, money being worth 5 %. OPERATION. Amount of $1 for 4 y. = $1.20 $480 $1.20 = 400 Since $1, at 5% interest, in 4 years, amounts to $1.20, it will require as many dollars to amount to $480, at the same rate, for the same time, as $1.20 is contained times in $480, or 400. RULE. Divide the given sum by the amount of $1 for the given time, at the given rate. To find the discount, subtract the present worth from the given sum. Examples. Find the present worth of 2. $250, due in 6 months, at 6 %. 3. $900, due in 72 days, at 7 %. Ans. $242.71+. What is Present Worth? Discount? Explain the operation. Repeat the Rule. How do you find the discount? * Optional. 4. $650, due in 1 year and 4 months, at 8 %. 5. $347.25, due in 2 years, 7 months, 15 days, at 6 %. What is the discount on 6. $672, due 2 years hence, at 6 % ? 7. $350.75, due in 93 days, at 6% ? Ans. $300. Ans. $72. Ans. $5.36+ 8. $750, due in 2 years, 3 months, 20 days, at 7% ? Ans. $104.23+. 304. Since the present worth corresponds to the principal, the debt to the amount, and the discount to the interest of the principal for the time and at the rate given, the rule also applies, when the time, rate, and amount are given, to find the principal. What principal will amount to 9. $1114.18, in 2 years, at 8 %? 10. $3641.20, in 66 days, at 7 %? 11. $145.67, in 123 days, at 6 % ? Ans. $960.50. Ans. $3595.04+. 12. $4748.10, in 3 years, 3 months, 9 days, at 5 % ? APPLICATIONS. Ans. $4080. 1. What is the present value of a note for $385, payable in 9 months without interest, money being worth 6 % ? Ans. $368.42. 2. What is the difference between the interest and discount of $1050, due 10 months hence, at 6 %? Ans. $2.50. 3. Bought goods for $1831.53 cash, and at once sold them for $1986.48, on credit of 6 months; how much did I make, money being worth 5% ? Ans. $106.49. 4. A man was offered a horse for $225, cash in hand, or for $230, payable in 9 months; if he accepts the latter, when money is worth 7 %, how much will he gain by the choice? Ans. $6.48. To what does the present worth correspond? The debt? The discount? To what does the rule apply? BANK DISCOUNT. 305. A Bank is a joint stock company, or an incorporation, for the purpose of receiving deposits, loaning money, or issuing notes or bills for circulation. 306. A Promissory Note is a written promise to pay ab solutely a certain sum of money, for value received. The FACE of a note is the sum made payable. DAYS OF GRACE are the three days usually allowed for the payment of a note, after the expiration of the time specified. In Pennsylvania four days are allowed. A note is nominally due at the expiration of the time named in it, and is legally due at maturity, or at the expiration of the days of grace. When the last day of grace occurs on Sunday, or a holiday, the note is payable the day before. The time when a note is nominally and when legally due may be indicated by writing the number of the days with a line between them. Thus, May 119. A note is discounted when bought for less than its face. The time to run, or term of discount, of a note, is the time from the day of discounting to the maturity. 307. Bank Discount is an allowance to a bank for payment of money on a note before it is due. It is the interest on the face of the note for the term of discount. The PROCEEDS, or AVAILS, of a note is the sum paid for it, or the face of the note less the discount. CASE I. 308. To find the bank discount or proceeds of a note. 1. What is the bank discount and proceeds of a note for $500, for 90 days, at 6 %? What is a Bank? A Promissory Note? The Face of a note? Days of Grace? When is a note legally due? What is Bank Discount? The Proceeds? The time to run? Interest of $500 for 93 d. = $7.75, discount. $500-$7.75 $492.25, proceeds. = RULE. Find the interest on the face of the note for the term of discount, at the given rate, and it will give the discount. The discount subtracted from the face of the note will give the proceeds. Notes discounted usually draw no interest till maturity. If, however, a note is at interest, the face of the note is the amount at maturity. The difference between bank and true discount is equal to the interest on the true discount. Examples. 2. A sixty days' note for $600 was dated and discounted on the same day, at 6%; required the discount and proceeds. Ans. Discount $6.30; proceeds $593.70. 3. A note for $250, in 4 months, was dated and discounted Dec. 31, at 1 % a month; required when due, and the amount of proceeds. Ans. Due April 30 May 3; proceeds $239.75. Find when due, time to run, discount, and proceeds, of the following notes: 4. $1650. New York, July 5, 1866. Four months after date, for value received, I promise to pay Horatio Sheridan, or order, one thousand six hundred fifty dollars at the Manhattan National Bank. [Stamp]. Discounted Sept. 5, at 7 %. Charles N. Thayer. Ans. Due Nov. 5|8; to run 2 mo. 3 d.; discount $20.217; proceeds $1630.183. Explain the operation. Repeat the Rule. How does bank discount compare with true discount? To what is their difference equal? 5. $5000. St. Louis, June 10, 1893. Ninety days after date, I promise to pay at the order of S. Clark & Co. five thousand dollars, value received. [Stamp.] Discounted July 13, at 6 % William Kaspar. Ans. Due Sept. 8; to run 60 d.; discount $50; proceeds $4950. CASE II. 309. To find the face of a note, its proceeds being given. 1. What must be the face of a note at 90 days, which, when discounted at 6 %, will give $492.25? OPERATION. Since $1 discounted for $.9845 the given time and rate gives $.9845 proceeds, there must be required to Proceeds of $1 for 93 d. = = give $492.25 proceeds, as many dollars as $.9845 is contained times in $492.25, or 500. RULE. Divide the proceeds of the note by the proceeds of $1, for the given time and rate. Examples. 2. Find the face of a four months' note which, when discounted at 1% a month, yields $239.75. Ans. $250. 3. The proceeds of a sixty days' note discounted at 6 %, are $593.70; required the face of the note. 4. I wish to obtain $3755 from a bank; what must be the face of the note, payable in 90 days, at 7 %? Ans. $3824.15+. 5. Find the face of a two months' note which, when discounted at 2% a month, yields $576. 6. A merchant owing $994.50, gave a 30 days' note, which was discounted at 6 % ; required the face of the note to pay the exact debt. Ans. $1000. Explain the operation. Repeat the Rule. |
