be not extinguished by payment, interest is to be cast upon that interest from the time it becomes due, up to the time of payment. 2. If the contract be for a sum payable at a specified time with interest, no interest becomes due till the time of payment arrives, and endorsements made before that time are to be applied exclusively to the principal. Rule 1. When the contract is for the payment of interest annually, and no payments have been made, find the interest of the principal for each year, separately, up to the time of payment; then find the interest of these interests, severally, from the time they become due up to the time of payment, and the sum of all the interests added to the principal will be the amount: but if payments have been made, find the amount of the principal, and also the amount of the payments to the end of the first year; subtract the latter amount from the former, and the remainder will be the principal for the second year; proceed in the saine way from year to year up to the time of pay. ment.* Examples. 1. A's note to B for $100, with interest annually, at 6 cent was dated January 1, 1820; what was due, principal and interest, January 1, 1824? 1st year. $100 X 6=$6 Int. 2 100*6= 6" 6X18=1.08 At the end of the first 3 100 X 6= 6" 6 X 12= .72 year, one year's interest 100 X 6= 6“ 6* 6= .36 =$6, is due, but as it is not paid, it draws interest Principal. 100. $24 Int. $2.16 Int. for the three following Int. of prin. 24. Int, of int. 2.16 years=$1.08. At the end of the second year, another year's inte rest is due, which draws interest for ? Amount. $126.16 Ans. years; and so on. per months for the year, which is endorsed on the note. Now if the interest be cast by the above method, there will be found due at the end of the year, $9384.798. But this is $14.798 more thau is justly due, as may be thus shown: it is plain that neither the 10000 dollars, nor the interest of it, is due till the end of the year, when their amount is 10600 dollars ; B is therefore at liberty to pay or not, before that time. Now suppose B keep back these several payments, and put them to interest till the end of the year; the first will amount to 210 dollars, the second to 208, the third to 206, the fourth to 204, the fifth to 202, and the sixth to 200; and their whole amount is (210+208+206+204+202+ 200)=1230, so B will have 1230 dollars at the end of the year towards extinguishing the amount of the debt, and $10600—1230 =9370, the sum justly due, which is $14,798 less than the former. This method allows compound interest, both upon the principal and payments, and they are compounded, that is, the interest becomes a part of the principal as often as the payments are made. * It will sometimes happen that when a note bas endorsements, there will be years in which no payments are made ; for which years the interest is to be found by the former part of the rule ; and also wł th mount of the payment is less than the interest of the principal, subtract the amount from that interest, and find the amount of the remainder up to the final payment, 2. B's note to C for $50, with interest annually, was dated Nov. 20, 1822, on the back of which were the following endorsements, viz. May 20, 1823, received $14, and Feb. 26, 1824, 830; what was due January 2, 1825 ? Prin. $50 Pay't. $14 Prin. $38.58 Pay't. $30 6 .7 Int. 3.00 .42 1.320 30. .067018 9.574 Am't. 53. Am't. 14.42 Am't. 40.894 Am't. 31.32 14.42 31 32 Ans. $9.641 due Jan. 2, 1825. 2 prio.38.58 3d prin. 9.574 3. D's note to E for $1000, 4. C's note to D for $200, with interest annually, was dat with interest annually, was dated May 5, 1822, on which the ed June 15, 1821, on the back of following payments were made; which was endorsed, Sept. 15, viz. Nov. 17, 1822, 8300; April 1821, 84, and Jan. 21, 1823, $15; 23, 1823, $50, and Aug. 11, 1823, | what was due Jan. 15, 1824? 8520; what was due June 5, Ans. 8217.196. 1824? Ans. $201.713. Rule 2. te; find When the contract is for a sum payable at a specified time, with interest, and payments are made before the debt becorr, the interest of the principal up to the first payment, & aside; subtract the payment from the principal, and find the st of the remainder up to the next payment, which interest set side with the former, and so on up to the time the debt becomes due, and the sum of the interests added to the last principal, will be the amount due at that time; after the debt falls due, the interest is to be extinguished annually, if the payments are sufficient for that purpose. Examples. 1. E's note to F for $75.25, payable in 2 years, with interest, was dated May 1, 1822, on which was endorsed Jan. 13, 1823, $25.25 ; what was due May 1, 1824? year. mo. day. Pay't. 25.25 Ist time. 8 12 2d prin. 50.00 X 7.8= 3.90 interest. 7.06 interests. 1824 4 1 20 time. 1 3 18 2. F gave his note to G for 3. G's note of 8365.37 was 85000 with interest, dated Sept. dated Dec. 3, 1817, payable Sept. 1, 1820, and payable January 1, 11, 1820 ; June 7, 1820, he paid 1824; on the 13th of June, 1822, 897.16; what was due when the he paid $2500, and Aug 25,1823, time of payment arrived ? 82500 more; what was due when Ans. $327.46. the time of payment arrived ? Ans. $715. QUESTIONS. 1. What is Interest? 10. What is the rule ? 2. How is it computed ? 11. What is Case III. ? 3. What is understood by the prin- | 12. What is the rule ? cipal ? 13. What is Case IV.? 4. What is the rate ? 14. What is the rule? 5. What is the amount ? 15. What is Case V.? 6. Of how many kinds is interest? 16. What is the rule ? 7. What is Simple Interest ? 17. What is Case VI.? any sum in Federal or English | 19. What the second? 20. What is the first rule? 9. What is Case II. ? 21. What the second ? icipal. 100 i fint, 2. Compound Interest. COMPOUND INTEREST is that which arises from making the interest a part of the principal at the end of each year, or stated time for the interest to become due. Rule I. Find the amount of the given principal for the first year, or to the first stated time for the interest to become due, by simple interest, and make the amount the principal for the next year, or stated period; and so on to the last. From the last amount subtract the given principal, and the remainder will be the compound interest required. Examples. 1. What is the compound in 3. What is the compound interest of $125 for 2 years and 6terest of $200 for 1 year, at 6 months,* at 6 per cent ? per cent, interest due every 4 $125 months ? Ans. 812.241. 6 4. What is the amount of 8236 7.50 Int. for 1st year. at 6 per cent, compound interest, 125. Prin. added. for 3 years, 5 months and 6 days? Ans. $288.387. 132.50 Amount for 1 year. 6 5. What is the amount of $150 7.9500 Int. for 2d year. at 6 per cept, compound interest, 132.50 Prin. added. for 2 years, the interest becom ing due at the end of every six 140.45 Amount for 2d year. inonths ? Ans. $168.826. 3 6. What is the compound in4.2135 Interest for 6 months. terest of $768 for 4 years, at 6 140.45 Principal added. Ans. $201.58. 144.6635 Amount for 2 ys. 6 mo. 125. Ist Prin. subtracted. 7. What is the compound in terest of 8560 for 3 years and 6 $19.663 Com. Int. required. months, at 6 per cent ? Ans. $126.977. 2. What is the compound interest of $100 for 4 at 6 Ans. $26.246. per cent ? per cent : Rule 2. By Decimals. 1. Find the amount of 1 dollar for 1 year at the given rate, and multiply this amount as many times into itself as the whole number of years, less by 1. 2. Multiply the last product by the principal, and the product will be the amount for the time; from which subtract the principal, and the remainder will be the interest required. * When there are months and days, first find the amount for the years, or stated periods. then find the amount of this amount for the months and days at simple interest. Any sum doubles at 6 per cent, compound interest, where the interest becomes due at the end of each year, in 11 years, 10 months and met days, and at simple interest in 16-17 years, per cent : per cent 4 per cent : Examples. 1. What is the compound in 2. What is the compound interest of $500 for 3 years, at 5 terest of $125 for 2 years, at 6 Ans. $15.45. 1.05 am't. of $1 for 1 year. 1.05 3. What is the amount of 760 525 dollars 50 cents, for 4 years, at 1050 1.1025 once into itself. Ans. $889.677. 1.05 55125 4. What is the amount of 110250 $6.66 for 2 years, at 9 per cent? 1.157625 twice into itself. Ans. 87.912. 500 principal. 578.812500 amount. 5. What is the amount of £720 500 for 4 years, at 5 per cent per an$78.812 interest required. Ans. £875 3s. 3 d. QUESTIONS. 1. What is Compound Interest? 3. What is the rule for Compound 2. What is the rule for finding Com Interest by decimals ? pound Interest? num? 3. Discount. Discount is an allowance made for the payment of money before it becomes due, and is the difference between that sum, due some time hence, and its present worth. The present worth of any sum, or debt due some time hence, is such a sum as would, in the given time, at the given rate, if put to interest, amount to the sum or debt then due.* * It is very evident that an allowance ought to be made for the payment of money before it becomes due, which is supposed to bear no interest till after it is due; for it is plain that the debtor, by keeping the money iu his own hands, could derive advantage from putting it to interest for that time, but by paying it before it is due, he gives that advantage to another. And hence some debtors will be ready to say, that since by not paying money till it becomes due, they may employ it at interest; therefore, by paying it before it is due, they shall lose that interest, and for that reason, all such interest ought to be discounted. But this is not true, for they cannot be said to lose the interest till the time the debt becomes due ; whereas we are to consider what is at present Jost by paying a debt due some time hence. Now the present worth of $106, due one year hence, discounting at 6 per cent, is evidently $100; for $100 put to interest, will amount to $106 at the end of the year, and just pay the debt, £0 that a debt of $106, due one year hence, discounting at 6 per cent, is justly satisfied by the present payment of $100. But the interest of $106, the time and rate as above, is $6.36, which exceeds the discount 36 cts. equal to the interest upon the discount for that time. The discount, therefore, of any sum, payable at some future time, is a sum, which put to interest for the given time and rate, will amount precisely to the interest on the given sum for that time. |