258. To calculate compound interest by the preceding Table. Multiply the amount of $1, or £1, for the given number of years, by the given principal, and the product will be the amount. Subtract the principal from the amount, and the remainder will be the compound interest. 11. What is the compound interest of $200 for 10 years, at 6 What is the amount ? Operation. $1.790848 Amt. of $1 for 10 years by table. 200 the given principal. $358.169600 amount required. $200 principal to be subtracted. Ans. $158.1696 interest required. 12. What is the amount of $350 for 12 years, at 4 per cent. per cent. ? per cent. ? 13. What is the amount of $469 for 15 years, at 3 What the interest ? 14. What is the interest of $500 for 24 years, at 6 per cent. ? 15. What is the interest of $650 for 30 years, at 7 per cent. ? DISCOUNT 259. Discount is the abatement or deduction made for the payment of money before it is due. For example, if I owe a man $100 payable in 1 year without interest, the present worth of the note is less than $100; for if $100 were put at interest for 1 year, at 6 per cent., it would amount to $106; at 7 per cent., to $107; &c. In consideration, therefore, of the present payment of the note, justice requires that he should make some abatement from it. This abatement is called Discount. Quest.—258. How is the amount found for any given number of years by the Table? How the interest ? 259. What is discount? What is the present worth of a debt, payable at some future time, without interest? 109 The present worth of a debt payable at some future time without interest, is that sum which, being put at legal interest, will amount to the debt, at the time it becomes due. Ex. 1. What is the present worth of $545, payable in 1 year and 6 months without interest, when money is worth 6 per cent. per annum ? Analysis.-The amount, we have seen, is the sum of the principal and interest. (Art. 234.) Now the amount of $1 for 1 year and 6 months, at 6 per cent., is $1.09; (Art. 237 ;) that is, the amount is 10% of $1, or the prinpal. The question then resolves itself into this : $545 is 10% of what principal ? If $545 is 1οο is 545= 109, or $5; and 100=$5 x 100, which is $500. Or we may reason thus : Since $1.09 (amount) requires $1 principal for the given time, $545 (amount) will require as many dollars as $1.09 is contained times in $545 ; and $545-$1.09= $500. That is, the present worth of $545, payable in 1 year and 6 months, is $500, which is the answer required. Proof.—$500 X.09=$45, the interest for 1 year and 6 months ; (Art. 247 ;) and $500+$45=$545 the given amount. Hence, 260, To find the present worth of any sum payable at a future time without interest. First find the amount of $1 for the time, at the given rate, as in simple interest; (Art. 247 ;) then divide the given sum by this amount, and the quotient will be the present worth. The present worth subtracted from the debt, will give the true discount. Obs. This process is often classed among the Problems of Interest, in which the amount, (which answers to the given sum or debt,) the rate per cent., and the time are given, to find the principal, which answers to the present worth. Quest.--260. How do you find the present worth of a debt? How find the discount? { $249.63 the discounworth; 2. What is the present worth of $250.38, payable in 8 months, when money is worth 6 per cent. per annum ? What is the discount? Operation. 1.04)250.38(240.75 The amount of $1 for the given 208 time and rate, is $1.04. (Art. 247.) 423 Dividing the given sum by this 416 amount, the .quotient $240.75, is 780 the present worth. And $250.38728 240.75= $9.63, the discount. $9.63 the discount. 520 3. What is the present worth of $475, payable in 1 year, when money is worth 7 per cent. per annum ? 4. What is the present worth of $175, payable in 2 years, when money is worth 7 per cent. per annum ? 5. What is the present worth of $1000, payable in 4 months, when the rate of interest is 6 per cent. ? 6. What is the discount on $750 due 6 months hence, when interest is 5 per cent. per annum? 7. A man sold a farm for $1800, payable in 15 months : what is the present worth of the debt, allowing the rate to be 6 per cent. ? 8. I have a note of $1150.33, payable in 9 months : what is its present worth at 7 per cent. interest per annum? 9. A merchant sold goods amounting to $840.75, payable in 6 months : how much discount should he make for cash down, when money is worth 7 per cent. ? 10. What is the discount on a draft of $2500, payable in 3 months, at 41 per cent. per annum ? 11. What is the present worth of $5000, payable in 2 months, at 6 per cent. per annum ? 12. What is the difference between the discount on $500 for 1 year, and the interest of $500 for 1 year, at 6 per cent. ? 21 BANK DISCOUNT. 261. It is customary for Banks in discounting a note or draft, to deduct in advance the legal interest on the given sum from the time it is discounted to the time when it becomes due. Bank discount, therefore, is the same as simple interest paid in advance. Thus, the bank discount on a note of $106 payable in 1 year, is $6.36, while the true discount is but $6. (Art. 260.) Obs. 1. The difference between bank discount and true discount, is the interest of the true discount for the given time. On small sums for a short period this difference is trifling, but when the sun is large, and the time for which it is discounted is long, the difference is considerable. 2. Taking legal interest in advance, according to the general rule of law, is usury. An exception is generally allowed, however, in favor of notes, drafts &c., which are payable within a year. The Safety Fund Banks of the State of New York, though the legal rate of interest is 7 per cent., are not allowed by their charters to take over 6 per cent discount in advance on notes and drafts which mature within 63 days from the time they are discounted.* 262. According to custom, a note or draft is not presented for collection until three days after the time specified for its payment. These three days are called days of grace. It is customary to charge interest for the days of grace. The banks, therefore, always calculate the interest for 3 days more than the time stated in the note. 13. What is the bank discount on a note of $500, payable in 1 year, at 6 per cent. ? What is the present worth? Quest.—261. How do banks usually reckon discount? What in effect is bank discount? Obs. What is the difference between bank discount and true discount? Is this difference worth noticing? How is taking interest in advance generally regarded in law? What exception to this rule is allowed ? 262. When is it customary to present notes and drafts for collection? What are these 3 days called? Is it customary to charge interest for the days of grace? *Revised Statutes of New York, Vol. III., p. 287. Operation. The interest of $500 for 1 year is $30. The " 3 days grace, is 0.25 Therefore the discount is $30.25 And the present worth is $500—$30.25=$469.75. 14. What is the bank discount on a draft of $250, payable in 4 months, at 7 per cent. ? 15. What is the bank discount on a draft of $375 for 30 days, at 6 per cent. ? 16. What is the bank discount on a note of $1000, payable in 60 days, at 5 per cent. ? 17. What is the present worth of $1160, payable in 90 days, discounted at a bank at 6 per cent. ? 18. What is the present worth of $750.36, payable in 5 months, at 41 per cent. ? 19. What is the bank discount of $1825.60, payable in 4 months and 15 days, at 6 per cent. ? 20. What is the present worth of a draft of $1292, payable in 60 days, at 7 per cent. discount? 21. What is the present worth of a draft of $5000, payable in 15 days, at 6 per cent. discount? 22. What is the present worth of a draft of $15000, payable in 3 days, at 6 per cent. discount? 23. What is the present worth of $1326, payable in 10 months, at 54 per cent. discount? 24. What is the bank discount, at 7 per cent., on a note of $836.81, payable in 90 days ? 25. What is the bank discount, at 8 per cent., on a draft of $1261.38, payable in 60 days? 26. What is the bank discount, at 6) per cent., on a draft of $10000, payable in 30 days? 27. What is the difference between the true discount and bank discount on $1000, payable in 5 years, at 6 per cent. ? 28. What is the difference between the true discount and bank discount on $100000, payable in 1 year, at 7 per cent. ? |