ILL. EX., II. What is the compound interest of $520, at 7%, for 4 y. 1 m. 24 d.? 13. What is the compound interest of $480 for 7 y. 10 m.? Ans. $277.829. 14. What is the amount of $100 for 2 y. 4 m., at 7% ? 15. What is the compound interest of $200 for 3 y. 2 m. 6 d.? 16. What is the amount of $221.075 for 3 y. 5 m., at 7% ? 17. What is the amount of $280 for 1 y. 10 m. 22 d., interest payable semi-annually? 18. What is the amount of $50 for 3 y. 13 d., at 5% ? 19. What is the compound interest of $896 for 2 y. 6 m. 15 d., at 5% ? 20. Find the compound interest of $300 for 3 y. 4 m. 12 d., at 7%. 21 Find the amount of £58 for 3 y. 5 m. 8 m. Ans. 70 £. 16 s. 1+d. 22* Find the compound interest of 75 £. 9 s. 9 d. for 4 y. 27 d., at 5%. 23* What is the difference between the compound and simple interest of $678.25 for 3 y. 6 m. 6 d. ? Ans. $11.488-. 24* What is the difference between the compound and simple interest of $100 for 1 y. 4 m., the compound interest payable semi-annually? 25 What is the difference between the amount of $175.08, at compound and at simple interest, from May 7, 1861 to Sept. 25, 1863, at 7%? 26. Find the difference between the simple and compound interest of 94 £. 12 s. 6 d. for 2 y. 6 m. 12 d., at 8% ? For Dictation Exercises, see Key. PROBLEMS IN INTEREST. 281. Since interest is always the product of the three factors, principal, rate, and time, it follows that to find the time, rate, or principal, when the interest and two of the other terms are given, it is only necessary to divide the interest by the product of the two given terms. 282. TO FIND THE TIME, WHEN THE INTEREST, PRIN CIPAL, AND RATE ARE GIVEN. ILL. EX. In what time will $300 gain $63 interest at 6% ? OPERATION. Int. of $600 for 1 y. = 3.5 yrs. Ans. The interest of $300 for 1 year at 6% is $18; it will require as many years for $300 to gain $63 as $18 is contained times in $63, which is 3 times. Ans. 31 y. Hence the RULE. To find the time, when the interest, principal, and rate are given: Divide the given interest by the interest of the principal at the given rate for 1 year. EXAMPLES. What time will be required 3. For $68.25 to gain $3.003, at 6%? 4. For $640 to gain $67.20, at 7% ? ? Subtract $280 from $301 to find the interest. Ans. 10 m. 9. In what time will $200 amount to $400, at 6% ? 10. In what time will $500 amount to $658.33}, at 6% ? 283. TO FIND THE RATE, WHEN THE INTEREST, TIME AND PRINCIPAL ARE KNOWN. ILL. EX. At what rate per cent. will $250 gain $25 in 2 years? If the interest of $250 for 2 y. at 1 per cent. is $5, it will require as many times 1% to gain $25 as $5 is contained times in $25, which is 5 times. Ans. 5%. Hence the RULE. To find the rate, when the interest, time, and principal are given: Divide the given interest by the interest of the principal for the given time at 1 per cent. 8. At what rate will $50 amount to $55.25 in 2 y.? 9. At what rate will $1000 amount to $1058.33 in 10 m.? 284. TO FIND THE PRINCIPAL, WHEN THE INTEREST, ILL. Ex. What principal will yield $42.50 interest in 8 m. 15 d. at 6%? OPERATION. Int. of $1 for 8 m. 15 d. at 6%,... $.0425) 42.50 (1000. The interest of $1 for 8 m. 15 d. at 6% is $.0425; it will require as many dollars of principal to gain $42.50 as $.0425 is contained times iu $42.50, which is 1000 times. Ans. $1000. Hence the RULE. To find the principal, when the interest, time, and rate are known: Divide the given interest by the interest of 1 dollar at the given rate for the given time. What principal will gain EXAMPLES. 1. $15 in 2 y. at 6% ? 2. $20 in 4 y. at 5% ? 3. $76.50 in 2 y. 6 m. at 3% ? 4. $1.705 in 7 m. 15 d. at 4% ? 5. $68.999 in 1 y. 4 m. 24 d. at 5% ? 6. $4.128 in 11 m. 14 d. at 6% ? Ans. $125. Ans. $100. NOTE. (4.128.057). Reduce dividend and divisor to thirds before dividing. Ans. $72. 7. What principal will be required to gain $24 in 60 days at 2% a month? 8. What principal must be on interest 2 y. 5 m. 29 d. at 6% to gain $89.40? 9. What is the principal which being on interest at 7% per annum, gains $62.50 semi-annually? 285. TO FIND THE PRINCIPAL, WHEN THE AMOUNT, TIME, AND RATE ARE KNOWN. ILL. EX. What principal will amount to $17.238 in 2 m. 12 d. at 7% ? OPERATION. The amount of 1 dollar for 2 m. 12 d. is $17.238 $1.014=17. $1.014; it will require as many dollars to amount to $17.238 as $1.014 is contained times in $17.238, which is 17 times. Ans. $17. Hence the RULE. To find the principal, when the amount, time, and rate are known: Divide the given amount by the amount of 1 dollar at the given rate for the given time. EXAMPLES. What principal will amount 1. To $870 in 7 y. 6 m. at 6% ? 2. To $537.50 in 2 y. 6 m. at 6%? Ans. $600, Ans. $467.393 3. To $2072.25 in 30 da. at 5% ? 5. To $100 in 3 y. 6 m. at 51% ? 6. To $343.75 in 2 y. 1 m. at 7% ? For Dictation Exercises, see Key. Ans. $2063.651+ Ans. $400. PRESENT WORTH AND DISCOUNT. 286. This subject is a practical application of Art. 285. It embraces all examples in which it is required to know what sum will equitably discharge a note or debt at a given time before it is due. 287. The Present Worth of any sum of money due at a future time without interest, is such a sum as put at interest at the given rate will amount to the debt when it becomes due. It is evident that where money is worth 6% a year, $106 due in one year is the same in value as $100 paid now; for $100 put at interest for 1 year will amount to $106. 288. Discount is that part of an obligation which is abated or given up when the payment is made before it becomes due, and should in justice equal the interest upon the present worth for the given time. 289. ILL. EX. What is the present worth of $210 due I year hence, money being worth 5% ? Here $210 is the amount of some principal for 1 year at 5%; $1 amounts to $1.05 in a year; hence it will require as many dollars to amount to $210 as $1.05 is contained times in $210, which is 200 times. Ans. $200. Hence the RULE. To find the present worth: Divide the given sum by the amount of 1 dollar at the given rate for the given time. The discount of the above ($210) is found by subtracting $200 from $210; this leaves $10, which is precisely the same as the interest of $200 for 1 year at 5%. Hence the RULE. To find the discount: Subtract the present worth from the given sum. |