EXAMPLES. I. In what time will $94.33cts. 9m.+66 rem., present money, amount to $100, admitting the discount to have been made at $6, per cent. per annum? $ c. m. 100=a 5.66034) 5.66034(1year=T. 5.66034 0 00000 2. In what time will $1165+50 rem. amount to $1200, at $6 per cent. per annum? Aus. 6 months. 3. In what time will $400, present money, amount to $500, at $10 per cent. per annum? Ans 2 years 6 months. 4. In what time will $5000 amount to $5150, at $8 per cent. per annum? Ans. 4 months. 5. In what time will $678 amount to $728.85cts. at $5 per cent. per annum ? Ans. 1 year 6 months. 6. In what time will $600 amount to $840, at $10 per cent. per annum? Ans. 4 years. 7. In what time will $3960.71cts.+17619 rem., present money, amount to $4895, at $12 per cent. per annum? CASE 4. Ans 1year 10 months 20 days. When A, P, and T are given, to find R. RULE.-R. tp EXAMPLES. 2. At what rate per cent. per annum will $1200, payable 6mo. hence, produce $1165+50 rem. in cash? Ans. $6 per cent. p. a. 3. At what rate per cent. per annum will $500, payable 24yrs. hence, produce $400 present money? Ans. $10 per c. p. a. 4. At what rate per cent per annum will $5150, payable 4 months hence, produce $5000 present money? Ans. $8 per. ct.! 5. At what rate per cent. per annum will $723.85cts. payable 1 years hence, produce $678 in Ans. $5 per cent. cash? 6. At what rate per cent. per annum will $840, payable 4 years bence, produce $600 present money? Ans. $10 per cent. ANNUITIES OR PENSIONS IN ARREARS, AT SIMPLE INTEREST. Annuities or Pensions are said to be in arrears when they are payable yearly, half yearly, or quarterly; and remain unpaid for any number of payments. NOTE. U represents the annuity or pension, &c., R, T, and A as before. 1750-tut. 2) 1400 700 .05=r 35.00 2. If the payment of a pension of $156 be omitted for 7 years; what will it amount to in that time, at $6 per cent, per annum? Ans. $1288.56cts. 3. If a house be let upon a lease for 8 years, at $80 per year, what will it amount to in that time at $4 per cent. per annum.? Ans. $729.60cts. 4. Suppose a salary of $333. 33 cts. a year be omitted for 6 years; what will it amount to in that time, at $41 per cent. per annum? Ans. $2225. NOTE.-When the annuities, pensions, &c. are to be paid half yearly or quarterly, as most generally they are-then, for half $385.00 a, or the amt. Ans. yearly payments, take half of the ratio, half of the annuity or yearly rent, and twice the number of years for R, U, and T. But, for quarterly payments, take one fourth part of the ratio, one fourth part of the annuity or yearly rent, and four times the number of years; then proceed as before. Add 350 tu. 3. A pension of $36 per year is omitted to be paid for 12 years; what is the amount in yearly, half yearly, and quarterly payments, at $6 per cent? Ans. The yearly amount is $574.56cts.; the half yearly amount $581.04cts., and the quarterly amount $584.28c. 4. The rent of a certain house at $50 a year is omitted to be paid for 15 years; what is the amount in yearly, half yearly, and quar terly payments, at $8 per cent.? Ans. The yearly amount is $1170; the half yearly amt. is $1185, and the quarterly amt. is $1192.50e. Ans. $70=u. 2. If the amount of a pension for 7 years be $1288.56cts., at $6 per cent., what is the pension? Ans. $156. 3. If a house be let on a lease for 8 years, and the amount for that time be $729.60cts., at $4 per cent., what is the yearly rent? Ans. $80. 4. If the amount of a yearly salary for 6 years be $2225, at $4.50cts. per cent., what is the Ans. $333.33 cts. salary? NOTE. When the payments are half yearly 4a must be divided; but, when they are quarterly, 8a must be divided as before. EXAMPLES. 1. If the amount of an annuity, payable half yearly for 5 years, at $5 per cent., be $389.371cts., what is the annuity? yrs. halfyrs. 5x2= 10=t. 05÷2=.025=r. .250=tr. 10=t. 2. If the amount of an annuiyears, ty, payable quarterly for 5 at $5 per cent., be $391.561cts., what is the annuity? Ans. $70=u. Ans. $70=u. 3. If the amount of a pension, payable every half year for 12yrs., at $6 per cent,, be $581.04cts., what is the yearly pension? Ans.$36. 4. If the rent of a house, payable every quarter for 15yrs., amount to $1192.50cts., at $8 per cent., what is the yearly rent? Ans. $50. CASE 3. When U, A, and T are given, to find R. 1. If an annuity of $70 per annum amount to $385 in 5 years, what is the rate per cent. per annum? $ $385=a. u=70 2 2. If a pension of $156 per annum amount to $1288.56cts. in 7 years, what is the rate per cent. per annum? Ans. $6 per cent. 3. If a house be leased for 8 years at $80 per year, and the amount for that time is computed at $729.60cts., what is the rate per cent. ? Ans. $4 per cent. per annum. at 4. If a salary $333.33 cts. a year amount to $2225 in 6 years, what per cent. was the interest computed? Ans. $4.50cts. p. c. p. a. NOTE. When the payments are half yearly, then 4a-4ut must be divided; and when they are quarterly, 8a-8ut must be divided as before. |