3.-Subtract the original principal from the last amount; the remainder will be the required compound interest. PROOF.-Multiply the interest of $1 or £1 for the given rate and time by the principal. A Table showing the compound interest on £1 or $1, for any number of years up to 10. 74. Find the compound interest on $100 for 3 years, at per Or, $157625 × 100 = $15.7625 Comp. Int. for 3 yrs. 75. Find the compound interest on $200 for 3 years, at 5 per cent per annum. Ans. $31.525. 76. Find the compound interest on $250 for 2 years at per cent per annum. Ans. $25.625. 77. Find the compound interest on $300 for 2 years at 6 per cent per annum. Ans. $37.08. 78. Find the compound interest on $350 for 3 years at 6 per cent per annum. Ans. $66.85+ 79. Find the compound interest on $316.75 for 3 years at 6 per cent per annum. Ans. $60.50+ 80. Find the compound interest on $472.25 for 4 years at 6 per cent per annum. Ans. $123.95+ 81. Find the compound interest on $750 for 3 years 6 months at 6 per cent per annum. Ans. $170.06. 82. Find the compound interest on $426 for 3 years at 7 per cent per annum. Ans. $95.868+ 83. Find the compound interest on $728.50 for 3 years 4 months at 7 per cent per annum. Ans. $184.767+ 84. Find the compound interest on $600 for 2 years 8 months at 7 per cent per annum. Ans. $119 85. Find the compound interest on £100 for 3 years at 5 per cent per annum. First year. Ans. £15 15s. 3d. £100 86. Find the compound interest on £216 for 2 years at 5 per cent per annum. Ans. £22 2s. 91d.+ 87. Find the compound interest on £360 for 3 years at 5 per cent per annum. Ans. £56 14s. 103d.+ 88. Find the compound interest on £374 12s. 6d. for 2 years at 6 per cent per annum. Ans. £46 6s. Od.+ 89. Find the compound interest on £482 10s. for 3 years at 6 per cent per annum. Ans. £92 3s. 31d.+ 90. Find the compound interest on £484 12s. for 2 years at 7 per cent per annum. Ans. £70 4s. 41d.+ 91. Find the compound interest on £1000 for 3 years 6 months at 7 per cent per annum. Ans. £267 18s. 4d.+ 92. If I loan to J. B. $300 at 6 per cent per annum, compound interest, how much will he owe me at the end of 4 years? Ans. $378.74+ 93. If I hold a bond from H. F., dated May 1, 1842, for $650, on which he was to pay me 6 per cent per annum yearly, and the interest be withheld, how much will he owe me May 1st, 1848? Ans. $922.04. 94. If I own a lot of ground worth now $1500, and the value of property increase at the rate of 7 per cent yearly, what will my lot be worth in 7 years from this time? Ans. $2408.67+ DISCOUNT. DISCOUNT is an allowance made for receiving money before it becomes due. I. To find the discount. RULE. As the amount (by Interest) of £100, or $100, is to the given sum, so is the interest on 100 to the dis count. II. To find the present worth. RULE: As the amount (by Interest) of £100, or $100, is to the given sum, so is 100 to the present worth. Subtract the present worth from the given sum, and the remainder will be the discount; or, subtract the discount, and the remainder will be the present worth. PROOF.-The amount of the present worth (by Interest) must equal the given sum; or, the interest on the present worth must equal the discount on the given sum. EXAMPLES. 1. What is the discount on $212, payable 1 year hence, interest 6 per cent per annum? $$ Ans. $12. 100+6 106...106: 212 :: 6=$12 Ans. $18. 2. Find the discount on $318, payable in 1 year, at 6 per cent per annum. 3. Find the discount on $535.60, payable in 6 months, at 6 per cent per annum. Ans. $15.60. What is discount? What are the rules? the note? the proof? 4. Find the discount on $475, payable in 3 years, at 6 per cent Ans. $72.46 per annum. 5. Find the present worth of $353.60, payable in 1 year 6 months, at 7 per cent per annum. Ans. $320. 7 6. Find the present worth of £478 16s., payable in 2 years, at per cent per annum. Ans. £120. 7. Find the present worth of £652 11s., payable in 9 months, at 7 per cent per annum. Ans. £620. 8. What is the present worth of $500, half payable in 6 months, and half payable in 12 months, at 6 per cent per annum? Ans. $478.56+ 9. What is the difference between the discount and the interest on $1200, payable in 2 years 6 months hence, at 6 per cent per annum? Ans. $27.26 NOTE.-Banks take interest for the use of their money. They always take it in the form of discount; i. e. they deduct the amount of the interest at the time of loaning the money. They allow 3 days grace, and for this they also charge interest. Grace is an extension beyond the time for which the note is written. ANNUITIES. AN Annuity is a sum of money payable yearly, half-yearly, or at other stated equal periods, by guardians, executors, government, loan offices, etc., to heirs, pensioners, etc. I. To find the amount of an annuity in arrears. RULE. Find the amount of each payment by the rules in Interest; the sum of the several amounts will be the required answer. II. To find the present worth of an annuity due some time hence. RULE. Find the present worth of each payment by the rules in Discount, and add them together for the whole present worth. NOTE. An annuity unpaid is said to be in arrears. What is an annuity? What is the rule for finding the amount of an annuity in arrears? What the rule for finding the present worth of an annuity payable some time hence? EXAMPLES. 1. If an annual payment of $100 be withheld for 4 years, what will be the amount due at the end of that time, allowing simple interest at 6 per cent per annum ? (I.) 118112+ 106 + 100 = Ans. $436. Or, 3+2+1= 6 years. 6 x 6 = 36. 36 + 400 = 436. J 2. If an annual payment of $150 remain unpaid for 3 years, what will be the amount due at the end of that time, allowing simple interest at 6 per cent per annum ? Ans. $477. 3. If an annuity of $60, payable half-yearly, be withheld 5 years, what will be the amount due at the end of that time, allowing simple interest at 7 per cent per annum? Ans. $694.50. 4. What is the present worth of an annuity of $200, payable in one, two, and three years, discount at the rate of 6 per cent per annum? (II.) Ans. $536.74. 5. What is the present worth of an annuity of $300, payable in one, two, three, and four years, discount at 5 per cent per annum ? Ans. $1069.31. 6. What is the present worth of an annuity of $450, payable in one, two, and three years, discount at 7 per cent per annum? Ans. $1187.20. 7. If an annual payment of $200 be withheld for 4 years, what will be the amount due at the end of that time, allowing compound interest at 6 per cent per annum? Ans. $874.92. 8. If I hire a house for $500 per year, payable in quarterly payments at the end of the quarter, what must I pay down at the commencement of the year to discharge the whole year's rent, discount off, at the rate of 6 per cent per annum ? Ans. $482.04. 9. If an annuity of $400, payable yearly at the end of the year, be in arrears years, what will be the amount due, allowing compound interest at 6 per cent per annum ? Ans. $1749.84+ 10. If an annuity of $500, payable yearly at the end of the year, be unpaid for 5 years, what will be the amount due, allowing compound interest at 6 per cent per annum? Ans. $2818.54+ |