On this note are the following indorsements. Sept. 1, 1845, received two hundred and fifty dollars. Nov. 1, 1846, received two hundred dollars. What was due June 1, 1847 ? Ans. $ 242.75. OPERATION. $ 600 x .075= 45.00, interest from June 1, 1844, to Sept. 1, 250 [1845. 350 X.07 = 24.50, interest from Sept. 1, 1845, to Nov. 1, 200 [1846. 150 x .035 = 5.25, interest from Nov. 1, 1846, to June 1, 74.75 $74.75, amount of interest. [1847. $224.75 remains due June 1, 1847. The above is the method of computing annual interest, when the contract is for a specified time. Note. — The above methods of computing annual interest are not only practised in the courts of Vermont, but a similar method has been adopted in some of the courts of New Hampshire; but it is not the method in Massachusetts. SECTION XXXIX. MISCELLANEOUS PROBLEMS IN INTEREST. PRINCIPAL, interest, and time given, to find the rate per cent. 1. At what rate per cent. must $ 500 be put on interest to gain $ 120 in 4 years? BY ANALYSIS. OPERATION. $ 500 The interest of $1 for the given time at one per cent. is 4 5.00 cents. $ 500 will be 500 times as much,= $ 500 X.04=$20.00. 20.00) 120.00(6 per cent. Ans. $120 will give 1200,= 6 per cent. Then, if $ 20 give 1 per cent. 120.00 RULE. – Divide the given interest by the interest of the given sum at 1 per cent. for the given time, and the quotient will be the rate per cent. required. 2. At what rate per cent. must $120 be on interest to amount to $133.20 in 16 months ? Ans. 85 per cent. 3. At what rate per cent. must $ 280 be on interest to amount to $ 411.95 in 6.1 years ? Ans. 71 per cent. Principal, interest, and rate per cent. given, to find the time. 4. How long must $ 500 be on interest at 6 per cent. to gain $120 ? OPERATION. BY ANALYSIS. $ 500 We find the interest of $1.00 at .06 the given rate for one year is 6 30.00)120.00(4 years, Ans. cents. $ 500 will, therefore, be 500 120.00 times as much, = $ 500 x .06 = $ 30.00. Now, if it take 1 year to gain $ 30, it will require about to gain $ 120, = 4 years, Ans. Rule. — Divide the given interest by the interest of the principal for 1 year, and the quotient is the time. 5. How long must $120 be on interest at 81 per cent to amount to $133.20 ?. Ans. 16 months. 6. How long must $ 280 be on interest at 71 per cent. to amount to $ 411.95 ? Ans. 63 years. Interest, time, and rate per cent. given, to find the principal. 7. What principal at 6 per cent. is sufficient in 4 years to gain $120 ? Rule. – Divide the given interest or amount by the interest or amount of $1 for the given rate and time, and the quotient is the principal. 8. What principal at 81 per cent. is sufficient in 16 months to gain $13.20 ? Ans. $120.00. 9. What principal at 7 per cent. is sufficient in 64 years to amount to $ 411.95 ? Ans. $280.00. SECTION XL. COMPOUND INTEREST. The law specifies that the borrower of money shall pay a certain number of dollars, called per cent., for the use of one hundred dollars for a year. Now, if this borrower does not pay to the lender this per cent. at the end of the year, it is no more than just that he should pay interest for the use of it, so long as he shall keep it in his possession; and this is called Compound Interest. 1. What is the compound interest of $ 300 for 3 years ? Ans. $ 57.30,4. First Method. Second Method. $ 300, principal. 5= )300 1.06 1= 15 18.00, interest for 1 year. 3 300 557.)318 318.00, amount for 1 year. 1= 15.90 1.06 3.18 19.08, int. for second year. 5=2)337.08 318 1= 16.85,4 3.37,0 357.30,4 300 20.22,48, int. for third year. 337.08 $57.30,4 357.30,48, amount for 3 years. Note. — 5 per cent. is 300 30 of the principal, and 1 per $57.30,48, compound int. for 3 yrs. cent. is { of 5 per cent. RULE. — Find the interest of the given sum for one year, and add it to the principal; then find the interest of this amount for the nesrt year; and so continue until the time of settlement. Subtract the principal from the last amount, and the remainder is the compound interest 2. What is the amount of $ 500 for 3 years ? Ans. $ 595.50,8. 3. What is the compound interest of $ 345 for 10 years ? Ans. $ 272.84,2. 4. What is the compound interest of $316 for 3 years 4 months and 18 days? Ans. $ 69.01,7. By the aid of the following Table, calculations are more easily effected than by the preceding rule. TABLE, Showing the amount of 1 dollar, or 1 pound, for any number of years un der 40, at 3, 4, 5, 6, and 7 per cent., compound interest. Years. 11 15 19 Years. 3 per cent. 4 per cent. 5 per cent. | 6 per cent. | 7 per cent. 1.030000/1.040000 1.050000 1.060000 1.070000 1.304773 1.423311|1.5513281 1.6894781 1.838459 1.753506 2.106849 2.526950 3.025599 3.616528 20 1.806111 2.1911232.653297 | 3.207135| 3.869685 21 1.860294 2.278768 2.785962 3.399563 4.140563 1.9161032.369918 2.925260 3.603537 4.430403 3.1670264.61636516.704751) 9.703507 13.994820 39 40 13.262037 4.8010207.039988 10.285717 11.974457 40 30 'To perform questions by the Table, multiply the amount of one dollar for the given rate and time found in the Table by the principal, and from the product subtract the principal, and the remainder is the compound interest. Note.- If there be months and days, find the amount for them on the number taken from the Table, before it is multiplied by the principal. EXAMPLES. 5. What is the compound interest of $ 360 for 5 years, 6 months, and 24 days? Ans. $138.14. OPERATION. 1.338225, amount of 1 dollar for 5 years. .034, ratio for 6 months and 24 days. 5352900 4014675 .045499650 1.338225 1.383724650, amount of 1 dollar for 5yrs. Omo. 24 days. 360 360 Ans. $ 4221.70,6. 7. What is the amount of $ 480 for 40 years ? Ans. $ 4937.14,4. 8. What is the interest of $ 300 for 10 years, 7 months, and 15 days ? Ans. $ 257.40,1. 9. What is the amount of $ 586 for 12 years, 1 month, and 29 days, at 5 per cent. ? Ans. $1060.99,5. 10. The probable number of blacks at this time (1835) in the United States is 2,500,000. Now, supposing their increase to be 25 per cent. for every 10 years, what will be their number in the year 1935 ? Ans. 23,283,057. 11. Supposing the annual increase of the people of color to be 2 per cent., how many must be sent out of the country each year, that their numbers might not increase ? Ans. 50,000. 12. What is the amount of $ 900 for 7 years, at 5 per cent. ? Ans. $1266.39. |