264. Compound Interest.* 1. When the unpaid interest is added to the principal, as it becomes due, to form a new principal on which interest is computed, the interest is called compound interest. Interest may be added to the principal annually, semiannually, quarterly, etc., according to agreement. The payment of compound interest cannot usually be enforced by law, but if the debtor is willing to pay compound interest, it may be collected without violating the law against usury. 2. Savings banks generally pay interest semiannually. When it is not collected by the depositor, it is added to his deposit and he is paid compound interest. 3. If interest is collected when due and reinvested at once at the same rate of interest, the result is the same as when compound interest is received. 4. Find the amount of $600 for 2 yr. 6 mo. at 8%, interest compounded annually. Find the difference between the compound interest and the simple interest. MODEL: $600 = principal for first year. 48 $648 = interest for first year. = amount, or principal, for second year. 51.84 interest for second year. = $699.84 = amount, or principal, for third year. 27.99 interest for 6 mo. = Compound interest = $727.83 – $600 = $127.83. Difference = = $120. $ 7.83. 5. If a man invests $1000 at compound interest at 6% when he is 30 years of age and keeps it earning at the same rate until he is 50 years of age, what will be the amount of the $1000 at that time? (Use table, p. 320.) * For table of compound interest, see Appendix, p. 320. 265. Bank Discount and Proceeds. 1. Banks usually collect interest in advance on sums loaned. Thus, if George White borrows $100 at a bank for 60 da. at 6%, his note will be made out for $100, and the bank will deduct from this amount the interest on $100 for 60 da. at 6%, or $1. Mr. White will receive $99. At the end of 60 da. he will pay the bank the face of the note, or $100. 2. If interest is collected in advance, how much money will a person receive at a bank on a note for $2000 for 60 da., if the bank charges 8% interest? 3. On April 8 J. J. Dow bought $ 600 worth of goods of D. C. Brown, on 90 da. time, giving his note for the amount without interest. On the same day D. C. Brown sold the note to a bank, the bank deducting 6% interest for the term of the note (90 da.). Find the amount received for the note by D. C. Brown. 4. Interest paid in advance upon the amount due on a note at its maturity is called bank discount. Bank discount is computed from the date of the purchase of the note by the bank to the legal date of maturity. Some banks include both the day of purchase and the day of maturity in the discount period. When days of grace are allowed, these are included in the discount period. 5. The sum paid for a note when sold is called the proceeds of the note. The proceeds on a note is the amount due at maturity, less the bank discount. 6. C. W. Smith held a note against R. E. Orr for $4000 for 60 da. without interest. After 20 da., he sold it to a bank at a discount of 6%; that is, the bank deducted 6% int. on the note for the 40 da. between its purchase and expiration. Find the bank discount and the proceeds. 7. On April 24, 1906, James J. Hall sold a horse to G. M. Bruce for $150, taking in payment his note for 1 year with interest at 6%. Find the amount of the note at maturity. 8. Mr. Hall (Ex. 7) needed money, so he sold the note to a bank on the same day, the bank discounting it at 6%. How much did Mr. Hall receive for the note? 9. If the note (Probs. 7 and 8) had been discounted at 8% instead of 6 %, what amount would Mr. Hall have received? 10. If the note (Probs. 7 and 8) had been discounted three months after date of issue, or on July 24, 1906, the bank would have deducted interest on the amount due at maturity ($159) for the exact number of days from July 24, 1906 to April 24, 1907 (7 da. + 31 da. + 30 da. + 31 da. + 30 da. + 31 da. + 31 da. + 28 da. + 31 da. + 24 da.), or for 274 da. Find the amount which Mr. Hall would have received. 11. A 90-da. note for $500, without grace, dated Aug. 5, 1905, with interest at 5%, was discounted at a bank on Aug. 25 at 6%. Find the day of maturity, the amount at maturity, the bank discount, and the proceeds. 12. A man borrowed $1000 of a bank for 1 yr. at 6%, paying interest in advance. 6% interest in advance on $1000 is equivalent to what rate paid at the end of the year? 266. Present Worth. 1. On Jan. 15, 1906, Frank Clark sold his farm for $4120 cash, and his neighbor, Henry Blair, sold his farm for $4120, on 6 mo. time, without interest. Did the two receive the same amount for their farms? 2. On the same day Mr. Clark (Prob. 1) loaned the amount received for his farm for 6 mo. at 6%. Find the amount due him at the end of 6 mo. Compare this amount with the amount due Mr. Blair for his farm on the same day. 3. At the end of 6 mo. each $1 received by Mr. Clark (Probs. 1 and 2) for his farm amounted to $1.03. Find how many dollars received on Jan. 15, 1906, would amount to $4120 in 6 mo. at 6%. Since $1 in cash amounts to $1.03 in 6 mo. at 6%, the number of dollars in cash that will amount to $4120 in 6 mo. at 6% is $4120 ÷ $1.03, or $4000. Prove that $4000 will amount to $4120 in 6 mo. at 6%. $4000 is the present worth of $4120 in 6 mo. at 6%. It is the sum which placed at interest for 6 mo. at 6% will amount to $4120. 4. Find the present worth of $406 in 90 da. at 6%. 5. If money is worth 5%, which is the lower price for a bill of goods, $1200 cash or $1210 on 60 da. time? 6. When money is worth 8%, what amount in cash is equivalent to $3600 due in 1 yr.? in 6 mo.? in 60 da.? 7. When money is worth 8%, what cash value is equivalent to $180 due in 60 da.? 8. The cash value of a sum due at a future time is its present worth. The difference between the present worth and the face of a sum due at a future time is called true discount. PART IV FORMS AND MEASUREMENTS* 267. 1. Lines are vertical, horizontal oblique \/ 2. These are right angles. J 3. A rectangle has four right angles. 4. These are right triangles. 5. These are acute angles. ^ V 6. These are acute-angled triangles. AD 7. These are obtuse angles. 8. These are obtuse-angled triangles. 9. Perpendicular (p) means at right angles to. 10. These figures have a base (b) and an altitude (a). 11. These lines are parallel. 12. These are quadrilaterals. and b a a b 13. These quadrilaterals are parallelograms. 14. These are rectangular prisms. *With complete reviews. |