PROBLEMS IN COMPOUND INTEREST. 319. The problems in compound interest are the same as those in simple interest, with the exception that the interest is compounded. There are five parts to be considered, the principal, rate, time, compound interest, and amount. I. The principal, rate, and time being given, to find the compound interest and amount. (307.) II. The time, rate, and compound interest being given, to find the principal and amount. (314.) III. The time, rate, and amount being given, to find the principal and compound interest. (315.) IV. The principal, time, and compound interest being given, to find the rate and amount. (316.) V. The principal, compound interest, and rate being given, to find the time and amount. (317.) The operations will be greatly facilitated by consulting the Compound Interest Table (p. 288). 1. What are the compound interest and amount of $200 for 3 years, at 5% ? Ans. Amt. $231.525. 2. What principal, at 6% compound interest, will gain $6180 in 2 years, and what will be the amount? 3. What principal, at 6% compound interest, will amount to $2382.032 in 3 years, and what will be the interest? Ans. Prin. $2000; Comp. Int. $382.032. 4. If $84.8428 compound interest is paid for the use of a principal of $ 700 for 3 years, what is the rate per cent? Ans. 4%. 5. In what time will $500 gain $72.45, at 7% compound interest? SOLUTION. Since $500 gains $72.45 in a certain time, $1, in the same time at the same rate, will gain of $72.45, which is $.1449. Consulting the table to find in what time $1 will gain $.1449, at 7%, we find it to be 2 years. 6. In what time will $300 gain $122.13, compound interest at 5% ? Ans. 7 years. PRAC. AR. 19 TRUE DISCOUNT. 320. True Discount is an abatement or allowance made for the payment of a debt before it is due. 321. The Present Worth of a debt, payable at a future time without interest, is such a sum as, being put at legal interest, will amount to the given debt when it becomes due. The True Discount is the difference between the whole debt and the Present Worth. EXAMPLES. 1. A owes B $321, payable in 1 year. What is the present worth of the debt, the use of money being worth 7%? What is the true discount? OPERATION. Amount of $1 = $1.07)$ 321 ($300, Present value. 321 $321 Given sum or debt. 300 Present worth. $21 Discount. SOLUTION.-The amount of $1 for 1 year is $1.07; therefore the present worth of every $1.07 of the given debt is $1; and the present worth of $321 will be as many dollars as $1.07 is contained times in $321. $321÷ $1.07 = $300, Áns. RULE.-I. Divide the given sum or debt by the amount of $1 at the given rate, for the given time, and the quotient will be the present worth of the debt. II. Subtract the present worth from the given sum or debt, and the remainder will be the true discount. The terms present worth, discount, and debt, correspond respectively to principal, interest, and amount. Hence, when the time, rate per cent, and debt (amount) are given, the present worth (principal) may be found by (315); and the true discount (interest), by subtracting the principal from the amount. 2. What is the present worth of $180, payable in 3 years 4 months, at 6% ? Ans. $150. 3. What is the present worth of a note for $ 1315.389, due in 2 years 6 months, at 7% ? Ans. $1119.48. 4. What is the present worth of a note for $ 866.038, due in 3 years 6 months and 6 days, when money is worth 8%? What is the discount? Ans. $190.15+, discount. 5. What is the present worth of a debt for $1005, on which $475 is to be paid in 10 months, and the remainder in 1 year 3 months, the rate of interest being 6% ? When payments are to be made at different times without interest, find the present worth of each payment separately and add the results. 6. I hold a note against C for $529.925, due Sept. 1, 1893. What must I discount for the payment of it to-day, Feb. 7, 1893, money being worth 6% ? Ans. $17.425. 7. A man was offered $ 3675 in cash for his house, or $4235 in 3 years, without interest. He accepted the latter offer. How much did he lose, money being worth 7%? Ans. $175. 8. A man, having a span of horses for sale, offered them for $ 480 cash in hand, or a note of $550 due in 1 year 8 months, without interest. The buyer accepted. the latter offer. Did the seller gain or lose thereby, and how much, interest being 6%? Ans. Seller gained $20. 9. What must be discounted for the present payment of a debt of $2637.72, of which $517.50 is to be paid in 6 months, $793.75 in 10 months, and the remainder in 1 year 6 months, the use of money being worth 7% ? Ans. $187.29+. 10. What is the difference between the interest and true discount of $130, due 10 months hence, at 10% ? Ans. $.831. BANK DISCOUNT. 322. A Bank is a corporation chartered by law for the purpose of receiving and loaning money. 323. A Promissory Note is a written or printed engagement to pay a certain sum, either on demand, or at a specified time. 324. Bank Discount is an allowance made to a bank for the payment of a note before it becomes due. If a banker is satisfied that a note is valid, and has ample security, he will cash it; that is, advance the sum due less the Bank Discount, which is simple interest upon the amount due for three days more than the time, at the legal rate. 325. The Face of a note is the sum made payable by the note. 326. Days of Grace are the three days usually allowed by law for the payment of a note after the expiration of the time specified in the note. 327. The Maturity of a note is the expiration of the days of grace; a note is due at maturity. The term of discount is the time from the discount of a note to its maturity. 328. Notes sometimes contain a promise of interest, which is reckoned from the date of the note, unless some other time is specified. 329. The transaction of borrowing money at banks is usually conducted in accordance with the following custom: the borrower presents a note, either made or indorsed by himself, payable at a specified time, and receives for it a sum equal to the face, less the interest for the time the note has to run. The amount thus withheld by the bank is in consideration of advancing money on the note prior to its maturity. 330. The Proceeds of a note is the sum received for it when discounted, and is equal to the face of the note less the discount. EXAMPLES. 331. Given the face of a note, to find the proceeds and bank discount. 1. What are the proceeds and bank discount of a note for $2000, due in 2 mo. 15 da. at 6% ? SOLUTION. = The time + 3 da. = 78 da. The interest of $1 for 78 da. $.013. The interest of $2000 = 2000 × $.013 = $ 26, bank discount. The face of the note the proceeds $1974, Ans. = = = $2000 bank discount, $26, RULE.-I. Compute the interest on the face of the note for three days more than the specified time; the result will be the discount. II. Subtract the discount from the face of the note, and the remainder will be the procee is. 2. What is the discount and what the proceeds of a note for $450, at 60 days, discounted at a bank at 6% ? Ans. Discount, $4.725; proceeds, $445.275. 3. What are the proceeds of a note for $368, at 90 days, discounted at the Bank of New York? Ans. $362.30. 4. What will I receive on my note for $475.50, at 60 days, if discounted at the Crescent City Bank, New Orleans? Ans. $471.33+. 5. What are the proceeds of a note for $10000, at 90 days, discounted at the Philadelphia Bank? Ans. $9845. |
