Find the proceeds, if this note was discounted at the bank, at 8%, May 29, 1903. 9. My note of $360, which will be legally due in 1 yr. 4 mo. 20 da., is discounted at a bank, at 8%. What rate of interest does the banker receive? NOTE. The difference between true discount and bank discount is equal to the simple interest on the true discount for the given time at the given rate. Illustrate this fact by solving the following example: 10. Find the difference between the true discount and the bank discount on $440, due in 1 yr. 8 mo., at 6%, not reckoning days of grace. III. ANNUAL INTEREST 350. Annual interest is simple interest on the principal, augmented by the simple interest on each interval's interest from the close of the interval to the time of settlement. EXAMPLE A note of $600.00 drawing 6% interest, payable annually, runs for 4 years and 3 months. Find the amount due at maturity, if no payments have been made. SOLUTION: Each year's interest will bear interest after it becomes due, as follows: I. 1. 1st year's interest for 3 years, 3 months. years, 3 months. Total 7 years. To the simple interest on the principal for 4 years, 3 months, we must add the interest on 1 year's interest for the sum of the above intervals, 7 years. 4. $600 + $153 + $15.12 = $768.12, amount due. Exercise XLII 1. A note of $350 drawing 5% interest, payable annually, runs 4 years, 6 months. Find the amount due at maturity, if no payments have been made. 2. A man bought $500 worth of goods on 9 months' credit; he paid for them at the end of 3 years, 3 months. Allowing 6% interest, payable annually, how much was due? 3. A gentleman holds six $1000 railroad bonds, due in 3 years, interest 6% payable semi-annually: no interest having been paid, what amount is owing him when the bonds mature?-R. N. H., p. 260. NOTE. Frequently annual or periodic interest is payable semiannually or quarterly. 4. Find the annual interest on $800 for 1 year, 9 months, at 5% per annum, payable quarterly. 5. The annual interest on a sum of money for 4 years, 6 months, at 5%, paid annually, was $85.75. What was the sum? SUGGESTION.-Find the annual interest on $1. 6. Find the amount due at the end of 5 years, 9 months, of a note of $1200, bearing interest at 6%, payable annually, if no payments have been made. REMARK. In some states, the law provides that unpaid annual interest shall bear interest at the legal rate. In the following problem, the unpaid interest bears the legal rate of interest. 7. In a state whose legal rate is 6%, H makes a note of $1250 for 3 yr. 3 mo., with interest at 8%, payable semiannually; he pays no interest; find the amount due at maturity.-S. & K., p. 197. IV. COMPOUND INTEREST 351. Compound interest is the interest that accrues by making the interest, due at the close of any interval, a part of the interest-bearing principal for the next succeeding interval. EXAMPLE Find the compound interest on $1 for 3 years at 5%, payable annually. SOLUTION: principal (P). rate (R). int. for 1st yr. = = the original principal. the compound int. for 3 years. A careful study of this example will show that the compound amount of $1, at any rate, for any number of years, equals (1 + R) raised to the power indicated by the number of years. Then to get the amount of n dollars, take In times the amount of $1. Using the initial letters, we have the following formulas: 352. The interest interval is generally a year, half-year, or quarter-year. The length of the interval is indicated by inserting annually, semi-annually, or quarterly. The half-interval rate = √1+ interval rate - 1. Thus, if the annual rate is 21%, the semi-annual rate √1.21 1= 1.10 1.10, or 10%. This fact may be illustrated thus: 1. Am't of $100 for 1 yr. at 21% annually = 1.21 × $100 = $121. 3... the semi-annual multiplier = √1.21, and the rate = √1.21-1. Similarly, it can be shown that the quarterly multiplier = TABLE Showing the amount of $1 at compound interest from 1 year to 20 years. Yr. 2 per cent. 3 per cent. 3 per cent. 4 per cent. 5 per cent. 6 per cent. 1.468534 12345 67899 1.159693 1.194052 1.229255 1.265319 1.188686 1.229874 1.272279 1.315932 1.218403 1.26677 1.316809 1.368569 1.248863 10 1.280085 1.343916 1.312087 1.384234 12 1.344889 1.425761 1.378511 11 13 14 1.412974 1.51259 1.103813 1.125509 1.147523 1.169859 1.304773 1.362897 1.423312 1.551328 1.689479 1.790848 1.806111 15 1.448298 16 1.484506 1.604706 1.733986 1.872981 2.182875 2.540352 17 1.521618 1.652848 1.794676 1.947901 2.292018 2.692773 18 1.559659 1.702433 1.857489 2.025817 2.406619 19 1.59865 1.753506 1.922501 2.106849 2.52695 20 1.638616 1.989789 2.191123 2.653298 2.854339 3.0256 3.207136 9 per cent. 10 per cent. 11 per cent. 12 per cent. 1.992563 2.143589 2.304537 2.475963 9 1.838459 1.999005 2.171893 2.357948 | 2.558036 2.773078 1.967151 2.158925 2.367364 2.593742 2.83942 3.105848 11 2.104852 2.331639 2.580426 2.853117 4.177248 4.784588 5.473565 3.151757 3.478549 3.49845 3.895975 3.883279 4.363492 4.31044 4.887111 5.05447 5.895091 6.130392 6.86604 3.379932 3.996019 4.71712 5.559917 6.543551 7.689964 19 3.616527 4.315701 20 3.869684 4.660957 5.141661 6.115909 7.263342 8.61276 5.604411 6.7275 8.062309 9.646291 |