What will $480 amount to in 6 years, at $5 per cent. per anAns. $643.24cts. 5m.+.9075 rem. num? 1. What principal will amount to $555.66cts. in 3 years at $5 per cent. per annum ? 1.05 cts.a. 1.157625)555.660000 ($480=P. Ans. 2. What principal will amount to $946.85cts. 7m.+72 rem. in 4 years, at $6 per cent. per annum? Ans. $720. 3. What principal will amount to $1672.78cts. 1m.+972 rem. in 5 years, at $6 per cent. per annum? : 4. What principal will amount to $643.24cts. 6 years, at $5 per cent. per annum? CASE 3. Ans. $1250. 5m.+9075 rem. in Ans. $480. EXAMPLES. 1. In what time will $480 amount to $556.66cts. at $5 per cent? t = $cts.=a. p=$480)555.660000(1.157625=r, which 3 involutions of r wherefore the time is 3 years. 2. In what time will $750 amount to $946.85cts. 7m.+72 rem. at $6 per cent. per annum? Ans. 4 years. 3. In what time will $1250 amount to $1672.78cts. 1m.+972 rem. at $6 per cent. per annum? Ans. 5 years. Ans. 6 years. 4. In what time will $480 amount to $643.24cts. 5m.+9075 rem. at $5 per cent per annum? RULE. CASE 4. When P, A, and T are given, to find R. t a tS then extract that root of r which is indicated rby the number of years in the question for r. EXAMPLES. t 1. At what rate per cent. will $480 amount to $555.66cts. in 3yrs? 480)555660000(1.157625=r, and the /1.157625=1.05 r. Ans. 2. At what rate per cent. will $750 amount to $946.85cts. 7m. +72 rem. in 4 years? Ans. $6 per cent. 3. At what rate per cent. will $1250 amount to $1672.78cts. 1m. +972 rem. in 5 years? Ans. $6 per cent. 4. At what rate per cent. will $480 amount $643. 24cts. 5 m.+ 9075 rem. in 6 years? Ans. $5 per cent. OF ANNUITIES OR PENSIONS, &c. IN ARREARS AT COMPOUND INTEREST. NOTE.-U represents the annuity, pension, &c., R, T, and A as heretofore. CASE 1. A. 2. What will an annuity of $250 per annum, payable yearly, amount to in 5 years, at $6 p. c.? Ans. $1409.27c. 3m.+.24rem 3. What will an annuity of $240 a year, payable yearly, amount to in 6 years, at $5 p. c.? Ans. $1632.45c. 9m.+.075 rem. 4. What will an annuity of $480 a year, payable yearly, amount to in 7 years, at $5 p. c.? Ans. $3908.16c. 4m.+.0575rem. 1. What annuity, being forborne 4 years, will amount to $344, 81 cents, at $5 per cent. per annum ? 17.24050000($80=u. Ans. .21550625 2. What annuity, being forborne 5 years, will amount to $1409. 27cts. 3m.+24 rem., at $6 per cent. per annum? Ans. $250. 3. What annuity, being forborne 6 years, will amount to $1632. 45cts. 9m.+075 rem., at $5 per cent, per annum? Ans. $240. 4. What annuity, being forborne 7 years, will amount to $3908. 16cts. 4m.+.0575 rem., at $5 per cent. per annum? Ans. $480. CASE 3. RULE. When U, A, and R are given, to find T. u OF THE PRESENT WORTH OF ANNUITIES, &c. AT COMPOUND INTEREST. NOTE.-P represents the present worth, U, T, and R, as before. CASE 1. When U, T, and R are given, to find P. 1. What is the present worth of an annuity of $80 a year, to continue 4 years, at $5 per cent. per annum discount? 4 $cts. $=u. 2 What is the present worth of a salary of $250 a year, to continue 5 years, at $6 per cent. per annum discount? Ans. $1053.10cts.. 3. What is the present worth of a pension of $240 a year, to continue 6 years, discounting $5 per cent. per annum for prompt pay.ment? Ans. $1218.16cts. 8m.+. 4. A superannuated officer has a pension of $480 a year allowed him for 7 years; what is it worth in present money, allowing the purchaser $5 per cent. discount? Ans. $2777.46cts. + 1. What annuity, to continue 4 years, may be bought with $288. 68cts., allowing $5 per cent. per annum for prompt payment? 1.21550625 1 4 Sub. 24065000 remainder rejected in 1st. case.. .21550625.) 17.24050000(80$-u. Ans. 2. I demand what annuity may be bought for 5 years, with $1053. 10cts.+ready money, allowing the purchaser $6 per cent. per annum for prompt payment? Ans. $250. 3. If the present worth of a lease, to continue 6 years, be $1218. 16cts. 8m.+what is the yearly rent, allowing $5 per cent. per annum for prompt payment? Ans. $240. 4. If the present worth of a pension, to continue 7 years, be $2777.46cts., what is the yearly income, allowing $5 per cent. per annum discount? Ans. $480. CASE 3. When U, P, and R are given, to find T. u RULE. = t tthen involve r, till it is=r and the EXAMPLES. 1. How long may a lease of $80 a year, be purchased for $283. 68cts. ready money, allowing the purchaser $5 per cent. for prompt payment? $283.63cts. p. 65.816 80.00000000000 24065000 rem. subtracted ) 79.99975935000(1.21550625=r, which is equal to 4 involutions of r, consequently the time is 4 years. 2. How long may an estate of $250 a year be rented for $1053. 10cts.+ in ready money, allowing $6 per cent. for prompt payment? Ans. 5 years. 3. How long may a pension of $240 a year be enjoyed for $1218. 16cts. 8m.+ allowing the purchaser $5 per cent. for prompt payment? Ans. 6 years. 4. How long may a salary of $480 a year be bought for $2777. 46cts.+ allowing 5 per cent. discount? Ans. 7 years. OF ANNUITIES, &c. IN REVERSION AT COMPOUND INTEREST. To find the present worth of an annuity, pension, &c. taken in reversion at Compound Interest.. RULE. 1. Find the present worth of the yearly income for the time of |