the three days of grace are always included. The amount named in a note is called the face of it. The PRESENT VALUE of a note is the difference between the face of the note and the discount. 230. There are two kinds of notes discounted at banks: 1st. Notes given by one individual to another for property actually sold these are called business notes, or business paper. 2d. Notes made for the purpose of borrowing money, which are called accommodation notes, or accommodation paper. Notes of the first class are much preferred by the banks, as more likely to be paid when they fall due, or in mercantile phrase, “when they come to maturity." To find the bank discount on a note, Add 3 days to the time which the note has to run before it becomes due, and calculate the interest for this time at the given rate per cent. EXAMPLES. 1. What is the bank discount of a note of $1000 payable in 60 days, at 6 per cent interest? This note will haye 63 days to run. Ans. 2. A merchant sold a cargo of cotton for $15720, for which he receives a note at 6 months: how much money will he receive at a bank for this note, discounting it at 6 per cent interest? Ans. $15240,54. 3. What is the bank discount on a note of $556,27 payable in 60 days, discounted at 6 per cent per annum? Ans. $5,840+. 4. A has a note against B for $3456, payable in three months; he gets it discounted at 7 per cent interest: how much does he receive? Ans. $62,496. 5. What is the bank discount on a note of $367,47, having 1 year, 1 month, and 13 days to run, as shown by the face of the note, discounted at 7 per cent? Ans. $29,0097+. What 230. How many kinds of notes are discounted at banks? distinguishes one kind from the other, and what are they called? Which kind is preferred? How do you find the bank discount on a note? 6. For value received I promise to pay to John Jones, four months from the 17th of July next, six thousand five hundred and seventy-nine dollars and 15 cents. What will be the discount on this, if discounted on the 1st of August, at 6 per cent per annum? Ans. 231. It is often necessary to make a note, of which the present value shall be a given amount. For example, if I wish to receive at bank the sum of two hundred dollars, for what amount must I give my note payable in three months ?* If we calculate the interest on one dollar for the time, which will be 3 months added to the 3 days of grace, and at the same rate per cent, this will be the bank discount on $1 payable in 3 months; and if this discount be subtracted from one dollar, the remainder will be the present value of one dollar, to be paid at the end of 3 months. Hence, Pres. val. of $1 pres. val. of note: $1 amt. of note. Therefore, to find the face of a note, due at a future time, and bearing a given interest, that shall have a known present value, Find the present value of $1 for the same time and at the same rate of interest, by which divide the present value of the note, and the quotient will be the face of the note. EXAMPLES. 1. For what sum must a note be drawn at 3 months, so that when discounted at a bank, at 6 per cent, the amount received shall be $500 ? Interest on $1 for the time, 3mo. and 3da.=$0,0155, which taken from $1, gives present value of $10,9845; then $500 0,9845 $507,872+ face of note. *The rule founded on the above well-known principle was, it is believed, first published by Roswell C. Smith, in his New Arithmetic. 231. What is often necessary in bank business? What will be the present value of one dollar due in 3 months? How will you find the face of a note, of a given present value, that shall be payable at a future time? PROOF. Bank interest on $507,872 for 3 months, including 3 days of grace, at 6 per cent =7,872, which being taken from the face of the note, leaves $500 for its present value. 2. For what sum must a note be drawn, at 7 per cent, payable on its face in 1 year 6 months and 14 days, so that when discounted at bank it shall produce $307,27? Ans. $344,59+. 3. A note is to be drawn having on its face 8 months and 12 days to run, and to bear an interest of 7 per cent, so that it will pay a debt of $5450: what is the amount? Ans. $5734,32+. 4. What sum, 6 months and 9 days from July 18th, 1846, drawing an interest of 6 per cent, will pay a debt of $674,89 at bank, on the 1st of August, 1846 ? Ans. $695,64+. 5. Mr. Johnson has Mr. Squires' note for $874,57, having 4 months to run, from July 13th, and bearing an interest of 5 per cent. On the 1st of October he wishes to pay a debt at bank of $750,25, and gives the note in payment: how much must he receive back from the bank? Ans. $118,85+. 6. What must be the amount of a note discounted at 6 per cent, having 4 months and 7 days to run, to pay a debt of $1475,50? Ans. 7. Mr. Jones, on the 1st of June, desires to pay a debt at bank by a note dated May 16th, having 6 months to run and drawing 7 per cent interest: for what amount must the note be drawn, the debt being $1683,75 ? Ans. $1740,61+. 8. What amount at the end of one year, with grace, interest at 5 per cent, will pay $1004,20 at bank? Ans. $1057,51+. 9. Mr. Wilson is indebted at the bank in the sum of $367,464, which he wishes to pay by a note at 4 months with interest at 7 per cent for what amount must the note be drawn? Ans. DISCOUNT. 232. If I give my note to Mr. Wilson for $106, pay. able in one year, the true present value of the note will be less than $106 by the interest on its present value for one year; that is, its true present value will be $100. The true present value of a note is that sum which being put at interest until the note becomes due, would increase to an amount equal to the face of the note. Thus, $100 is the true present value of the note to Mr. Wilson. The discount is the difference between the face of a note and its true present value. Thus, $6 is the discount on the note to Mr. Wilson. To find the true present value of a note due at a futurė time, find the interest of $1 for the same time; then, $1+its interest: $1 given sum: its present value. Hence, to find the present value of any sum, Add one dollar to its interest for the given time and di vide the given amount by this number, and the quotient will be the present value. EXAMPLES. 1. What is the present value of a note for $1828,75, due in one year, without grace, and bearing an interest of 4 per cent per annum? $1+its interest for the given time=$1,045: Hence, $1828,75÷$1,045-$1750 the present value. PROOF. Int. on $1750 for 1 year at 41 per cent=$78,75 Add principal 232. What is the true present value of a note? What is the true discount? How do you find the true present value of a note due at a future time? 2. A note of $1651,50 is due in 11 months, without grace, but the person to whom it is payable sells it with the discount off at 7 per cent: how much shall he receive? Ans. $1551,918+.' 3. How much ought Mr. Ready to pay in cash for his note of £36, due 15 months hence, without grace, it being discounted at 5 per cent ? Ans. £33 17s. 73d.+. 233. When payments are to be made at different times, find the present value of the sums separately, and their sum will be the present value of the note. 4. What is the present value of a note for $10500, on which $900 are to be paid in six months; $2700 in one year; $3900 in eighteen months; and the residue at the expiration of two years, all without grace, the rate of interest being 6 per cent per annum? Ans. 5. What is the discount of £4500, one-half payable in 6 months and the other half at the expiration of a year, without grace, at 7 per cent per annum? Ans. £223 58. 8d.+. 6. What is the present value of $5760, one-half payable in 3 months, one-third in 6 months, and the rest in 9 months, without grace, at 6 per cent per annum? Ans. $5620,175+. 7. Mr. A gives his note to B for $720, one-half payable in 4 months and the other half in 8 months, without grace: what is the present value of said note, discount at 5 per cent per annum? Ans. $702,485+. 8. What is the present value of £825 payable as follows: one-half in 3 months, one-third in 6 months, and the rest in 9 months, without grace, the discount being 6 per cent per annum? Ans. £804 19s. 5d.+. 9. Bought goods for £750 ready money, and sold them for £900 payable by a note at 6 months, without grace: now, if I discount the note at 6 per cent per annum, will I make or lose? Ans. 233. When payments are made at different times, how do you find the true present value? |