of the principal and time, the quotient is the rate; thus, 6 18 100 x 1 = rate. COR. 3.-If the interest is divided by the product f the rate and time, the quotient is the principal ; thus, 6 = 6 x 10 = $100 = principal. TO X 13 PROBLEMS. 360 1. What is the interest of $540 at 6% for 3 yr. 4 mo. 20 da. Ans. $540 X 16 X = $109.80, Interest for 3 yr. 4 mo. 20 da. 2. The principal is $540, the rate 6%, and the interest $109.80; what is the time? $109.80 109.80 Ans. 540 X 160 = 37 315 = 3 yr. 4 mo. 20 da. 32.40 3. The principal is $540, the time 318 yr., and the interest $109.80; what is the rate ? 109.80 109.80 109.8 109.8 Ans. 540 x 315 540 x fi 30 x 61 1830.0 3100 = 1, rate. To 4. The time is 315 yr., the rate 6%, and the interest $109.80; what is the principal ? $109.80 109.80 Ans. = 109.80 x 30 = $540.00. if X 16 306 1.80 61 EXAMPLES. 1. The principal is $1250, the rate 6%, and the interest $173.75 ; what is the time? Ans. 2 yr. 3 mo. 24 da. 2. The principal is $625, the time 278 years, and the interest $86.871; what is the rate ? Ans. 6% 3. The time is 218 years, the rate 6%, and the interest $260.623 ; what is the principal ? Ans. $1875.00. 4. The principal is $600, the rate 7%, and the interest $57.75; what is the time? Ans. 1 yr. 4 mo. 15 da. 5. The principal is $600, the rate 8%, and the interest $105.60; what is the time? Ans. 2 yr. 2 mo. 12 da. 6. The principal is $600, the time 18 years, and the interest $57.75 ; what is, the rate ? Ans. 7%. 7. The principal is $600, the time 21 years, and the interest $105.60; what is the rate ? Ans. 8%. 8. The time is 14 years, the rate 7%, and the interest $57.75 ; what is the principal ? Ans. $600. 9. The time is 23 years, the rate 8%, and the interest $105.60; what is the principal ? Ans. $600. 10. What is the interest of $6000 at 9% for 5 yr. 6 mio. 18 da. ? Ans. $2997. 11. What is the interest of $6000 at 6% for 5 yr. 6 mo. 18 da. ? Ans. $1998. 12. What is the interest of $6000 at 3% for 5 yr: 18 da. ? Ans. $999. 13. What is the interest of $6000 at 4% for 5 yr. 6 mo. 18 da. ? Ans. $1332. 14. What is the interest of $6000 at 5% for 5 yr. 6 mo. 6 18 da. ? Ans. $1665. 6 mo. REM.—In the computation of interest we find the interest equal to the product of the principal, rate per cent, and time. By using the initial letters for these, we get convenient formulas ; thus, Let P = principal, r = rate per cent, t = time, and I= interest; we have the equation (1.) Pxrxt = I. Divide both members by Ń x t, I (2.) · P = p xt Principal equal to interest divided by the product of rate and time. Rate equal to interest divided by the product of principal and time. Time equal to interest divided by the product of principal and rate. ENUNCIATION OF THE FORMULAS. 1. The interest of a sum of money is equal to the sum, called principal, multiplied by the rate and the time. 2. The principal is equal to the interest divided by the product of the rate and the time. 3. The rate is equal to the interest divided by the product of the principal and the time, and then reduced to hundredths. 4. The time is equal to the interest divided by the product of the principal and the rate. The four formulas enable us to determine any one of the four quantities when the other three are known. PROBLEMS. 1st FORMULA.—The principal is $750, the rate 6%, time 8 months. What is the interest ? 20 FORMULA.— The interest is $30, the rate 6%, and the time 8 months. What is the principal ? 3D FORMULA.—The interest is $30, the principal $750, and the time 8 months. What is the rate ? r = $30 750 X in = 3% = 180 = 6%, Rate. 1. Compute the interest on $5464.50, at 5%,for 1 year 9 months and 18 days. Ans. $491.805. 2. Compute the interest on $5464.50, at 8%, for 1 year 9 months and 18 days. Ans. $786.888. 3. Compute the interest on $5464.50, at 10%, for 1 year 9 months and 18 days ? 4. The interest is $630, the rate 6%, and the time 18 months. What is the principal ? Ans. $7000. 5. The interest is $540, the rate 9%, and the time 24 months. What is the principal ? Ans. $3000. 6. The interest is $600, the rate 5%, and the time 30 months. What is the principal ? 7. The interest is $300, the principal $2400, and the time 30 months. What is the rate ? Ans. 5%. 8. The interest is $560, the principal $3000, and the time 32 months. What is the rate ? Ans. 7%. 9. The interest is $140, the principal $1500, and the time 16 months. What is the rate ? 10. The interest is $270, the principal $3000, and the rate 6%. What is the time? Ans. 13 years. 11. The interest is $360, the principal $2400, and the rate 8%. What is the time? Ans. 224 months. 12. The interest is $66, the principal $500, and the rate 6%. What is the time? 13. The principal is $440, the interest $88, and the time 4 years. What is the rate ? Ans. 5% 14. The principal is $650, the interest $78, and the rate 6%. What is the time? Ans. 2 years. 15. The interest is $48, the rate 4%, and the time 3 years. What is the principal? Ans. $400. 16. In what time will any snm of money double itself at 6% simple interest ? I P 1 1 = = 1x 100 = 164 years. Pxr Рxr re 16 REM.—When the principal is doubled, the interest is equal to the principal ; that is, I = P. |