EXAMPLES. 1. What will $540 amount to in 3y. 4mo. 12da., at 6 per cent. compound interest? what will be the compound interest? 100 = Analysis. Since the simple interest of any sum of money at 6 per cent. equals of that sum, i. e., since a year's interest at 6 per cent. equals 1 of the principal, and since any principal must equal the whole or 10% of itself, it follows, that the AMOUNT (principal and interest,) will equal 100+ 18 to 106 of the principal for 1 year. Now, the principal under consideration is $540, to find the amount of which, (for 1 year at 6 per cent.,) we say, first, if the whole () of the principal equals $540, then 10% of the principal will = 188 of $540 = to $51240 = to $572.40 AMOUNT for the first year, or PRINCIPAL for the second year. Second, if the whole (4) of the principal = $572.40, or $5734°, then 188 of the principal will 108 of $57840 to $6067440 10000 = to $606.744, AMOUNT for the second year, or PRINCIPAL for the third year. Third, if the whole (1) of the principal = $606.744 = to 3600744, then 10% of the principal, will 108 of $606744 to $64314864 to $643.15 nearly, being the AMOUNT for the third year, or PRINCIPAL, the amount of WHICH must be found for the remainder of the time, i. e., for 4mo. 12da. Now, the interest of any sum of money, or principal, for 4mo. 12da. (132da.) = 6000 of that principal, and the whole principal-8888 of itself, and therefore, the AMOUNT will be equal to 6888+100% to 3 of the principal, for the same time, and since the principal is equal to $643.15 = to $64315, it follows, that if the whole principal () = $61335, 13 then of the principal will = 8133 of $61335 = to 6000 $394379580 to $6572293 $657.30 AMOUNT of $540, 600000 for 3y. 4mo. 12da., or ANSWER to the first demand in the question; lastly, $657.30-$540= $117.30, being the compound INTEREST for the whole time, or ANSWER to the second requirement of the question. 1000 100000 132 10000 6132 100 The above ANALYSIS serves to prove the correctness of the RULE, since the whole process has been conducted in exact accordance with ITs provisions. The same may be done by EQUATIONS. Thus : GIVEN QUANTITY †, or the whole PRINCIPAL. REQUIRED QUANTITY, 18 of the principal, or GIVEN QUANTITY }, or the whole PRINCIPAL. 100 Second year, EQUIVALENT, $572.40 $57240. GIVEN QUANTITY, or the whole PRINCIPAL. Third year, EQUIVALENT, $606.744=$6 606744 608744. Required quanTITY, 18% of the principal. 06 prin. $. Months and days of fourth year, GIVEN QUANTITY, †, or the whole PRINCIPAL. 6132 REQUIRED QUANTITY, 3 of the principal, or amount for 4 months, 12 days. 64315 SWER, or amount for 3 years, 4 months, 12 days. Lastly, $657.30 — $540 = $117.30, 2d ANSWER, or compound interest for the whole time as required to be done. Now bear in mind the GIVEN and REQUIRED QUANTITIES, as above, and we may shorten the process, thus : 4th. 6132 6132 64315 6572993 Dols. then,6000-6000 100 = 10000 =657.30, amount for the whole time, or first ANSWER. Lastly, $657.30 $540 =$117.30, second ANSWER, or compound interest for the whole time, as required by the conditions of the question. 2. I gave my note for $725.48, dated June 26th, 1837, payable in 9 months; but the holder gave me my own time, provided I would allow him compound interest, at 7 per cent., what amount did I pay to cancel said note, on the 4th of July, 1840? Solution.-From the 26th of June, 1837, to the 4th of July, 1840, is 3 years, 8 days, from which take 9 months, and there remains 2y. 3mo. 8da., or 2y. 98da. We have seen that the interest of $1 for 1 year at 7 per cent. equals $7 or $.07, and hence, the amount of $1 for 1 year, at 7 per cent. $1.07. Now, first, if $1 for 1 year at 7 per cent. amount to $1.07, then $725.48 will amount to 725.48 times $1.07 to $776.263+; second, if $1 for 1 year, at 7 per cent. amount to $1.07, then $776.263 will amount to 776.263 times $1.07 = to $830.60. Lastly, it has been shown that the interest of $1 for 98 days at 7 per cent. = = 686 or $.019+, and hence, the AMOUNT of $1 for 98 days at 7 per cent. equals $1.019, wherefore, the AMOUNT of $830.60 for 98 days at 7 per cent., will equal 830.60 times $1.019 to $846.48+. ANSWER. When the learner can analyze correctly, and give the reasons for what he does, he may proceed as follows: 776.2636 amount of $725.25 for 1 year. 54338452 7762636 830.602052 amount of $776.26+ for 1 year. 7475418468 830602052 $846.483490988 amount of $830.60+ for 98 days, or, the amount of $725.48 for 2 years 3 months, 8 days = $846.48+ ANSWER. When these examples have been studied carefully, the pupil will be prepared to furnish the ANSWERS to the following QUESTIONS FOR EXERCISE. 1. What is the amount of $150 at 6 per cent., for 2 years, at compound interest? What is the compound interest? 2. What will $250 amount to in 3 years, at 6 per cent. PER ANNUM, compound interest? 3. What is the compound interest of $450 for 4 years, at 6 per cent. PER ANNUM? 4. What is the amount of $300 for 2 years, at 6 per cent. compound interest? 5. A man gave a note, payable in 6 months, for $250, which he allowed to run 3 years over the time without pay. ing either principal or interest, how much did it amount to, allowing compound interest at 6 per cent. PER ANNUM? 6. What will $450 amount to in 3 years, 4 months, at 6 per cent. PER ANNUM compound interest? 7. What will $500 dollars amount to in 2 years, 3 months, 10 days, at 6 per cent. PER ANNUM, compound interest? 8. What is the compound interest on $475 for 3 years, 5 months, 18 days, at 6 per cent. PER ANNUM? 9. What will $1000 amount to in 2 years, at 5 per cent. compound interest? 10. What is the amount of $650 for 3 years, 3 months, 12 days, at 4 per cent, compound interest? 11. What will 25£. 10s. 6d. amount to in 2 years, at 6 per cent. compound interest? NOTE. Reduce the shillings and pence to the decimal of a pound, and then proceed with the calculation, after which reduce the decimal back to shillings, &c., again. 12. What would 1125£. 15s. 8d. amount to in 3 years, 4 months, 12 days, at 6 per cent. compound interest? 13. What will 112£. 9s. 9d. amount to in 4 years, 7 months, 16 days, at 7 per cent. compound interest? 14. A merchant gave a note, dated July 3d, 1809 for $4562.50, the payment of which was delayed till the 1st of January, 1815, what did the note amount to, allowing compound interest, at 4 per cent. PER ANNUM? BANK DISCOUNT. 1. BANK DISCOUNT is an allowance made to a BANK for the ready payment of a NOTE, due some time hence. 2. A BANK is a company of persons chartered (legally authorized,) to discount, or pay NOTES not yet due. NOTE.-Before a note is negotiable in bank, it must have the name of a second person written on the BACK, who thereby becomes the ENDORSER. If the note is not paid at maturity, the law requires that it shall be protested, (declared against,) by the proper officer, on the third day after it be comes due, in order to bind the endorser for the payment. |