4. $142.56 due 2 yr. hence at 4 per cent? 5. 6. $122.94 due 4 mo. 27 da. hence at 6 per cent? 7. 8. 9. 10. $731.52 due 3 yr. 4 mo. hence at 6 per cent? $1323.70 due 7 mo. 15 da. hence at 5 per cent? What is the discount of $195.87 due 1 yr. 5 mo. 19 da. hence, at 6 per cent per year? Direction. Find what part of the debt the discount is, and get that part of $195.87. For proof, subtract the discount thus found from $195.87, and see if the interest of the remainder for the given time equals the discount. We may also get the discount by finding the present worth, and subtracting it from the debt. What is the discount of 11. 12. 13. 14. 15. $3946.11 due 2 yr. 5 mo. 15 da. hence at 6 per cent? $179.96 due 2 yr. 3 mo. 6 da. hence at 4 per cent? 16. I own a note for $976, payable on demand with interest, and another for $1034.56, payable in just 1 year, with interest afterward. Allowing money to be worth 6 per cent per year, which debt is justly worth the most at the present time, and how much the most? Which will be worth the most at the end of the year? Which will be worth the most at the end of 6 months? Which will be worth the most at the end of 2 years? 17. If two notes are given on the same day, one for a certain sum due at a future time, with interest afterwards, and the other for the true present worth of the first note, payable on demand with interest, their true values will be the same at the time they are given, and also at the time the second becomes due; but at all other times they will differ. At any time between the day of their date and the day when the first note becomes due, the true value of the second note will be greater than that of the first; but at any time after the first note becomes due, the true value of the first note will be greater than that of the second. Show why this is so. 197. Business Method of Discount. (a.) Business men are usually willing to allow on money paid for goods before it is due, a discount equal to, or greater than, its interest from the time of payment to the time when, by the conditions of the sale, it would have become due. Thus, when only the interest of the debt is discounted, $824 due in 6 months, interest being 6 per cent per year, is regarded as worth $824 .03 of $824 = $824 - $24.72 $799.28, whereas it ought to be worth $800. (b.) This is always an advantage to the person owing the money, as it enables him to pay his debt for less than the sum which, put at interest, would amount to the debt at the time it would become due. (c.) It is common to deduct as much as five per cent from the face of a bill due in four or six months, and even more is sometimes deducted. (d.) The present worth thus obtained may be called the ESTIMATED PRESENT WORTH, to distinguish it from the TRUE PRESENT WORTH, obtained by the method explained in 196. 1. I owed a debt of $8692, payable June 1, 1852; but my creditor, offering to allow me discount estimated by the business method at the rate of 6 per cent per year, if I would pay the debt Jan. 1, 1852, I borrowed money for the purpose at 6 per cent interest. June 1, 1852, I paid the amount of the borrowed money. What was my gain by the transaction? 2. Owing a debt of $1545, due in 6 months, when money is worth 6 per cent per year, what shall I gain by hiring money enough to pay it now, allowing the usual business discount on the debt, and then paying the borrowed money with interest, when the original debt would otherwise have become lue? 3. At 6 per cent per year, what is the difference between the bank discount and the true discount of a note for $2059.40, payable in 60 days? * 4. Received for my note of $600, payable in 6 months, its true present worth. How much more did I receive on it than I should have received at a bank, money being worth 6 per cent? How much interest money shall I have gained, when the note becomes due, over what I should have gained on the present worth, as determined at the bank? 5. For how much must a note, payable in 30 days, be given, that, when discounted at a bank, $900 may be received on it, money being 6 per cent? 33 Solution. The money received on a note discounted at a bank equals the sum for which the note is given, minus its interest for the time before it becomes due. Since, at 6 per cent, the interest for 30 days and grace, or 33 days, = 6880-2000 of the principal, the sum received must equal 2888 – zódo 1888 of the face of the note. Therefore the face of the note = 2988 of the sum received on it, = = 1989 = $904,977, or, as it would in practice be considered, 6. How much would be received at a bank on a note for $904.98, payable in 30 days? NOTE. The above example suggests the method of proving the 5th. 7. For how much must a note payable in 3 months be given, that, when discounted at a bank, $1000 may be received on it, money being worth 6 per cent per year ? 8. For how much must a note payable in 6 mo. be given, that, when discounted at a bank, $1800 may be received on it, money being worth 6 per cent per year? * Remember that three days' grace are always allowed, unless the contrary is specified. 9. Obtained at a bank, on my note payable in 6 mo., money enough to buy 20 acres of land at $100 per acre. The day my note at the bank became due, I sold the land for $2062.32 cash. Did I gain or lose by the transaction, and how much, money being worth 6 per cent per year? 10. Obtained at a bank, on my note payable in 4 months, money enough to buy 20 acres of land at $100 per acre. The day the note became due, I sold the land for cash, at such rate that the price of 18 acres was just sufficient to pay the How much did I gain by the transaction, money being worth 6 per cent? note. 11. Bought goods to the amount of $864.27 on a credit of 6 months; but the seller offering to deduct 5 per cent from the face of the bill if I would pay cash, I hired the requisite amount of money, giving my note payable in 6 months, with interest at 6 per cent per year, to be reckoned from date. For how much less than the value of the original bill could I pay the amount of this note? 12. I owed $800, due in 6 months; but my creditor offering to deduct per cent of the debt for cash, I paid $330 down. How much did I still owe? Suggestion. Since 5 per cent of the debt was to be deducted for cash, the cash payment would be 95 per cent, = 18, of the part of debt it would cancel; or the part cancelled would be of the cash paid. 13. I owed $900, payable in 4 months; but my creditor offering to deduct 4 per cent of the debt for ready money, I paid $696 down. How much did I still owe? 198. To find the Rate. Problems in which, the principal, interest, and time being given, we are required to find the rate, rarely occur in business life. The following solutions illustrate the principles which apply to them. 1. At what rate per cent must $648 be on interest to gain $81.873 in 2 yr. 3 mo. 17 da. ? Solution. The principal being equal to 648,000 mills, and the interest to 81,873 mills, the interest is 81873 = 648000 2 yr. 3 mo. 17 da. = 27 mo. 17 da. = 827 da. 9097 9097 9097 72000 of the principal. If the interest for 827 1 da. = 20 of the principal, the interest for 360 9097 827 72000 day must equal 27 yr., or 360 da., must · 20% = .052 = 51 = 2. $624 gains $74.88 in yr. 2 mo. 12 da. 199. To find the Principal from the Interest. Problems in which, the interest, rate, and time being given, we are required to find the principal, are, like those in the last article, of rare occurrence. 1. What principal on interest at 6 per cent will gain $37.47 in 1 yr. 3 mo. ? Solution. 15 mo. = = At 6 per cent per year, the interest of any principal for of the principal. If $37.47 is 4 of the principal, of the principal must equal of $37.47, and the principal must equal 40 times the last result, or 4o of $37.47, which is $449.60. 2. What principal on interest at 8 per cent will gain $26.18 in 1 yr. 4 mo. 15 da. ? 16 12 yr. = Solution. - Since 1 yr. 4 mo. 15 da. = 16 mo. = of 1 yr., the interest must equal 11 of 8 per cent, or 11 per cent of the principal. If $26.18 is 11 per cent of the principal, 1 per cent of the principal must be TT of $26.18, which is $2.38, and 100 per cent, or the principal, must equal 100 times the last result, which is $238. What principal on interest 3. At 6 per cent will gain $8.73 in 5 mo.? 4. At 6 per cent will gain $4.77 in 1 yr. 5 mo. 20 da. ? |