10. If I buy a horse for $150, and a chaise for $250, and se! the chaise for $350, and the horse for $100, what is my gaiu per cent. ? A." $ ,125=124 per cent. 11. If I buy cotton at 15 cents a pound, and sell it for 16ide. cents, what should I gain in laying out $100 ? A. $10. 12. Booght 20 barrels of rice for $20 a barrel, and paid for freight 50 cents a barrel ; what will be my gain per cent. in selling it for $25,62% a barrel ? A. 25 per cent. 1 LXX. The Principal, Rate per cent., and Interest being given, to find the Time. 1. William received $18 for thu interest of $200 at 6 per cent. ; how long must it have been at interest ? The interest on $200 for 1 yr. at 6 per cent. is $12; hence $18; 12 = 14 years, the required time, Ans. Q. What, then, is the RULE ? A. Divide the given interest by the interest of the principal for 1 year at the given rate, the quotient will be the time required, in years and decimal parts of a year. 2. Paid $36 interest on a note of $600, the rate being 6 per cent.; what was the time ? 3. Paid $200 interest on a note of $1000; what was the time, the rate being 5 per cent. ? A. 4 years. 4. On a noto of $60, there was paid $9,18 interest, at 6 per cent; how long was the note on interesi? A. 2,55 yrs. = 2 yrs. 6 mo. 18 da. A. 1 year. COMPOUND INTEREST. II LXXI. 1. Rufus borrows of Thomas $500, which ho agrees to pay again at the end of 1 year, together with the interest, at 6 per cent.; but, being prevented, he wishes to keep the $500 another year, and pay interest the same as beforo. How much interest ought he to pay Thomas at the end of the tiyo years ? In this example, if Rufus had paid Thomas at the end of the first year, the Interest would have been $500 X 6 =$30, which, added to the principal, $500, thus, 500+30,=530, the sum or amount justly duo Thomas at the end of the first year; but, as it was not paid then, it is evidert, that, for the next year, 2d year,) Thomas ought to receive interest on $530, (being the amount of the first year). The interest of $530 for 1 year is 530 X 6= $31,80, which, added to $530, = 561,80, the amount for 2 years • hence, $561,80 --- $500=$61,80, jompound interest, the Answer. This mode of computing interest, although strictly just, is not authorized by Q. When the interest is added to the principal, at tho ond of 1 ycar, and on this amount the interest calculated for another year, and so on, what is it culled? A. Compound Interest. Q. How, then, 'may it be defined? A. It is interest on both principal and interest. Q. IVhat is Simple Interest ? A. It is the interest on the principal only. Hence we derive the following RULE. 1. How do you proceed? A. Find the amount of the princibal for the 1st year, by multiplying as in simple interest; ther of this amount for the 2d, and so on. II. How many times do you multiply and add ? times as there are years: the last result will be the amouni III. How is the compound interest found? A. By subtract 'ng the given sum or first principal from the product. As maig More Exercises for the Slate. 2 What is the compound interest of $156 for 3 yrs.? # 156 given sum, or first principal. 6 10,516896 = compound interest 3d year, and =first principal subtracted. Ans. $ 29,798 rejecting the three last figures, as of trifting value 3. What will be the amount of $500 for 4 years, at compound interest ? A. $631,238 40+ At 10 What is the difference between the simple interest of $200 4. What is the amount of $500 for 4 years, at simple interesı ? A. $620. 5. What will be the amount of $700 for 5 years, compound interest? A. 936,757 t. 6. What will be the amount of $700 for 5 years, at simple interest? A. $910. 7. What will be the amount of $1000 for 3 years, at compound interest? (1191016) $1500 for 6 years ? (21277786) $2000 for 2 years ? (224720) $400 for Ý years ? (601452) A. $6167,44616 8. What is the compound interest of $150 for 2 years ? (1854) $1600 for 4 years ? (4149631) $1000 for 3 years? (191016) $5680. for 4 years ? (1490869), $500 for 3 years? (95508) A. $2215,89615+. 9 What is the compound interest of $600,50 for 2 years, at 2 per cent.? (242602) Åt 3 per cent. ? (365704) At 4 per cent. ? (490008) At 5 per cent. ? (6155:12) At 7 per cent. ? (870124) . 331,50 I. for 3 years, and the compound interest for the same time? A. $2,203 20. 11. What is the compound interest of. $600 for 2 years 6 months ? In calculating the compound interest for months and days, first find the amount for the years, and on that amount calculate the interest for the months and days; this interest, added to the amount for the years, will be the interest required. 1. $94,33,47: 12. What is the compound interest of $500. for 3. years 4 mo. ? A. 107,41815+: 13. What is the difference between the simple and compound interest of $200 for 3 years ? (22032) For 4 years 6 mo.? (60702) For 2 years 8 mo. 15 da. ? (17706) A. $10,044. As the amount of $2 is twice as much as $1, $4,4 tunes as much, &c., hence, we may make a table containing the amount of the it. Q?$1, for several years, by which the amount of any sumi may be easily found for the same time. Years. 1 TABLE, Showing the amount of 1.€, or $1, for 20 years, at 5 and 6 per cent., at compound interest. 5 per cent. 6 per cent Years. 6 per cent. 6 per cent. 1,05000 1,06000 11 1,71033 1,89829 2 1,10250 1,12360 12 1,79585 2,01219 3 1,15762 1,19101 13 1,88564 2,13292 4 1,21550 1,26247 141,97993 | 2,26090 5 1,27628 1,33822 15 2,07892 | 2,39655 6 1,340091,41851 16 2,18237 2,54035 7 1 1,40710 1,50363 | 17 2,29201 2,69277 8 1,47745 1,59384 18 2,40661 2,85433 9 1,55132 | 1,68947 19 2,52695 | 3,02559 10 1,62889 1,79084 20 2,65329 | 3,20713 per cent. ? 14. What is the compound interest of $20,15 for 4 years, at 6 By the Table, $1, at 6 per cent. for 4 years, is $1,26247, X $20,15= $25,438, amount, from which $20,15 being subtract ed, leares $5,288170 to 15. What is the amount of $10,50, at 5 per cent for 2 years? (115762) For 6 years? (140709) ' For 8 years? (155132) For 15 years ? (215280) For 17 years? (240661) For 20 years ? (278595). $114,914 16 t, A. Any sum, at simple interest, will double itself in 16 years 8 months; but at compound, in a littlo more than half that time ; that is, in 11 years, 8 months and 22 days.. Hence, we sce that there is considerable difference in a few pears, and when compound interest is permitted to accumulate for ages, it imounts to a sum almost incredible.. If i cent had been put at compound'interest at the cominencement of the Christian eta, it would have amounted, at the end of the year 1827, to a sum greater than could be contained in six miltions of globes, each equal to our earth in magnitude, and all of so.id go.d, while the simple interest for the same time would have amounted to on.ý about one dollar. The following question is inserted, more for the sake of exemplifying the preceding statemont, than for the purpose of its solution. The amount, lowever, at compound interest, may be found, without niuch perplexity, by ascertaining the amount of 1 cent for 20 years, found by the Table, then making this ainount the principal for 20 years more, and so on for the whole number of years. 16. Suppose 1 cent bad becn put at interest at the commencemert of the Christian era, what would it havo amountod to at simple, and what at comround interest, at the end of the year 1827 ? A. Simple, $1,106 48 ; con pound $172616474047552529470760914974711959076620354,68 nearly. EQUATION OF PAYMENTS. 1 LXXII. Q. What is the meaning of equation? A. The art of making equal. Q: What is equation of payments? A. It is the method of fir.ding an equal or mean time for the payment of debts, due at Gifforent times. 1. In how many months will $1 gain as much as $2 will gain in 6 months ? A. 6 X 2= 12 months. 2. How long will it take $1 to gain as much as $5 will gain in 12 months ? A. 60 months. 3. How many months will it take $1 to be worth as much as the use of $10, 20 months ? A. 200 inonths. 4. A merchant owes 2 notes, payable as follows: one of $8, to be paid in 4 months; the other of $6, to be paid in 10 months, but he wishes to pay both at once : in what timo ought he to pay them? 4 X8=32; therefore, $8 for 4 mo. = $1 for 32 mo., and 10 X 6=60; therefore, $6 for 10 mo.= $1 for 60 mo. 14 92 'Therefore, he might have $1, 92 months, and he may keup $14, Ti part as long; that is, 74 of 92 inonths, which 18 92: 14,=6 mo. 1314 da., Ans. Q. Hence, to find the mean time of payment, what is the Rule? A. Multiply each payment by the time, and the sumi of these several products, divided by the sum of the payments, will be the answer. Note This rule proceeds on the supposition, that what is gained by keeper ing the money after it is due, is cqual to what is lost by paying it before it is But this is not exactly truc, for the gain is equal to the interest, while the loss is equal only to the discount, which is always less than the interest However, the error is su trißing, in most cases which occur in business, as not to make any material difference in the result 5. A owes B $200 to be paid in 6 months, $300 in 12 months, $500 in 3 months; what is the equated time for the payment of the whole ? A. 61%. 6. What is the equated time for paying $2000, of which $400 is due in 3 months, $360 in 5 months, $600 in 8 months, and the balance in 9 months ? A. 6.2008=627 months. 7. A merchant owes $600, payable as follows: $100 at 2 months, $200 at 5 nionths, and the rest at 8 months; but he wir hes to pay the whola debt at one time: what is the just time for said payment? A. 6 months. 8. I owe as follows, viz. to A $1200, payable in 4 months; to B $700, payable in 10 months ; lo C $650, payahle in 2 years u $idod, magabie in 34 years, to E $1270, payable in 20 due |