In what time will 2. $40 gain $10 at 5% ? 3. $500 gain $100 at 4%? 4. $25 gain $20 at 6%? 5. $1000 gain $250 at 5%? 6. $5 gain 90 cents at 6% ? 7. $50 gain $12 at 10%? WRITTEN EXERCISES. 583. 1. In what time will $840 gain $78.12 at 6%? 2. Will $175.12 gain $6.43 at 6%? 3. Will $1000 amount to $1500 at 71%? RULE.-Divide the given interest by the interest of the given principal, at the given rate for 1 year. FORMULA.-Time = Interest ÷ (Prin. × Rate). 4. In what time will $8750 gain $1260 at 2% a month? 5. How long must $1301.64 be on interest to amount to $1522.92 at 5%? 6. How long will it take any sum of money to double itself at 3%, 5%, 6%, 71%, and 10%, respectively? At 100%, any sum of money will double itself in 1 year; hence to double itself at 10%, it will require as many years as 10% is contained times in 100%, or 10 yr. 7. How long will it take any sum to triple itself at 4%, 5%, 7%, 8%, and 121%, respectively? 8. In what time will the interest of $120, at 8%, equal the principal? Equal half the principal? Equal twice the principal? COMPOUND INTEREST. 584. Compound Interest is interest not only on the principal, but on the interest added to the principal when it becomes due? 585. 1. What is the comp. int. of $500 in 2 yr. at 6%? ANALYSIS.-The simple interest of $500 for 2 yr. is $60; the interest of the first year's interest, $30, for the second year is $1.80, which, added to $60, gives $61.80, the compound interest. Or, The interest of $500 for 1 yr. at 6% is $30, and the amount is $530, which is the principal for the second year; the interest of $530 for 1 yr. at 6% is $31.80, which added to $530 gives $561.80, the final amount; and deducting $500, the original principal, gives $61.80, the compound interest. What is the compound interest 2. Of $600 for 2 yr. at 5%? | 4. Of $300 for 2 yr. at 10%? 3. Of $100 for 2 yr. at 7%? 5. Of $1000 for 2 yr. at 5%? What is the amount at compound interest, 6. Of $800 for 2 yr. at 5%? | 8. 7. Of $2000 for 2 yr. at 10%? 9. WRITTEN Of $400 for 2 yr. at 4%? Of $500 for 2 yr. at 8% ? EXAMPLES. 586. 1. What is the comp. int. of $750 for 2 yr. at 6%? OPERATION. $750 Prin. for 1st yr. $795 Prin. for 2d yr. $842.70 Total amount. $92.70 Compound int. ANALYSIS. Since the amount is 1.06 of the principal, the amount at the end of the first year is $795, which is the principal for the 2d year, and the amount at the end of the 2d year is $842.70. Hence, by subtracting the given principal, $750, the result is the compound interest, $92.70. 2. What will $350 amt. to in 3 yr. at 7%, comp. int.? 3. What is the compound int. of $1200 for 3 yr. at 5% ? RULE.-I. Find the amount of the given principal for the first period of time at the end of which interest is due, and make it the principal for the second period. II. Find the amount of this principal for the next period; and so continue till the end of the given time. III. Subtract the given principal from the last amount, and the remainder will be the compound interest. When the time contains months and days, less than a single period, find the amount up to the end of the last period, and compute the simple interest upon that amount for the remaining months and days, which add to find the total amount. 4. What will $864.50 amount to in 4 yr. at 8%, compound interest? 5. What is the compound interest of $680 for 2 yr. at 7%, interest being payable semi-annually? 6. What is the compound interest of $460 for 1 yr. 5 mo. 18 da. at 6%, interest payable quarterly? 7. What will be the amount of $1250 in 3 yr. 7 mo. 18 da. at 5%, interest being semi-annual? 8. Find the compound interest of $790 for 9 mo. 27 da. at 8%, payable quarterly. The computation of compound interest may be abridged by using the following table. To use the table, multiply the given principal by the number in the table corresponding to the given number of years and the given rate. If the interest is not annual, reduce the time to periods, and the rate proportionally. Thus, 2 yr. 6 mo., by semi-annual payments. at 7%, is the same as 5 yr. at 3%; and 1 yr. 9 mo., quarterly payments, at 8%, the same as 7 yr. at 2%. 587. TABLE showing the amt. of $1, at 21, 3, 31, 4, 5, 6, 7, 8, 9, 10, 11, and 12%, compound int., from 1 to 20 years. Yrs. 24 per cent. 3 per cent. 3 per cent. 4 per cent. 5 per cent. 6 per cent. 1 2 3 4 5 6 7 8 9 10 1.035000 1.040000 1.025000 1.030000 1.265319 1.340096 1.418519 1.188686 1.229874 1.272279 1.315932 1.407100 1.502630 1.218403 1.266770 1.316809 1.368569 1.477455 1.598848 1.248863 1.304773 1.362897 1.423312 1.551328 1.689479 1.280085 1.343916 1.410599 1.480244 1.628885 | 1.790848 11 1.312087 1.384234 1.459970 1.539454 1.710339 1.898299 12 1.344889 1.425761 1.511069 13 1.378511 1.468534 1.563956 14 1.412974 1.512590 1.618695 1.448298 1.557967 1.675349 15 1.601032 1.795856 2.012197 1.665074 1.885649 2.132928 1.731676 1.979932 2.260904 1.800944 2.078928 2.196558 1.484506 1.604706 1.733986 1.872981 2.182875 2.540352 1.521618 1.652848 1.794676 1.947901 2.292018 2.692773 1 559659 1.702433 1.857489 2.025817 2.406619 2.854339 1.598650 1.922501 2.106849 2.526950 3.025600 1.989789 2.191123 2.653298 3.207136 16 17 18 19 20 1.638616 1.753506 Yrs. 7 per cent. 8 per cent. 9 per cent. 10 per cent. 11 per cent. 12 per cent. 12345 67840 10 1.070000 1.080000 1.090000 1.100000 1.110000 1.120000 1.144900 1.166400 1.188100 1.210000 1.232100 1.254400 1.225043 1.269712 1.295029 1.331000 1.267631 1.404908 1.411582 1.464100 1.518070 1.573519 1.538624 1.610510 1.685058 1.762342 1.771561 1.870414 1.973822 1.828039 1.948717 2.076160 2.210681 1.838459 1.999005 2.171893 2.357948 2.558036 2.773078 1.967151 2.158925 2.367364 2.593742 2.889420 3.105848 11 2.104952 2.331639 2.580426 2.853117 3.151757 3478549 12 2.252192 2.518170 2.812665 3.138428 3.498450 13 2.409845 2.719624 3.065805 3.452271 3.888279 14 2.578534 2.937194 8.341727 3.797498 4.310440 15 2.759031 3.172169 3.642482 4.177248 4.784588 16 2.952164 3.425943 3.970306 4.594973 5.310893 6.130392 17 3.158815 3.700018 4.327633 5.054470 5.895091 6.866040 18 3.379932 3.996019 4.717120 5.559917 6.543551 7.689964 19 3.616527 4.315701 5.141661 6.115909 7.263342 8.612760 20 3.869684 4.660957 5.604411 6.727500 8.062309 9.646291 9. Find by the table the compound interest of $950 for 1 yr. 5 mo. 24 da., at 10%, interest payable quarterly. OPERATION. 1 yr. 5 mo. 24 da. = 5 quarters of a year +2 mo. 24 da. Amount for 5 yr. at 21% 1.131408 of principal. = = $950 × 1.131408 = $1074.837, amount for 1 yr. 3 mo. = $1099.916-$950 $149.916, compound interest. 10. Find the amount, at compound interest, of $749.25 for 10 yr. 4 mo., at 7%, interest payable semi-annually. 11. What sum placed at simple interest for 3 yr. 10 mo. 18 da., at 7%, will amount to the same as $1500 placed at compound interest for the same time, and at the same rate, payable semi-annually? 12. At 8%, interest compounded quarterly, how much will $850 amount to in 1 yr. 10 mo. 20 da. ? 13. What will $500 amount to in 20 yr. at 7%, comp. int.? 14. A father at his death left $12500 for the benefit of his only son, 14 yr. 8 mo. 12 da. old, the money to be paid him when he should be 21 years of age, with 6% interest compounded semi-annually. What did he receive? ANNUAL INTEREST. 588. Annual Interest is interest on the principal and on each year's interest remaining unpaid, but so computed as not to increase the original principal. It is allowed in the case of promissory notes and other contracts which contain the words, "with interest payable annually," or with 'compound interest." In such cases, the interest is not compounded beyond the second year. |