LESSON 29 Finding the Principal When the Time, Rate, and Interest Are Given EXAMPLE: What principal will yield $8.70 in 90 days at 6%? Interest on $1.00 for 90 days at 6% = 11; Proof: Int. on $580. for 90 days at 6% TXR = 3 × 180, or $230; I = $8.70; $8.70 ÷ $280 2009 $8.70 X 200, or $580., Ans. = EXAMPLE: The amount due at the maturity of a 30-day 6% note is $452.25; what is the principal? Interest on $1.00 for 30 days at 6% is 5 mills; therefore, each $1.00 amounts to $1.005. If all the principal amounted to $452.25 there were as many dollars as $1.005 is contained times in $452.25. 450 times; therefore, the principal is $450., Ans. As you have learned, four elements principal, rate per cent, time, and interest-are concerned in every interest example; therefore, if any three of these elements are given, the fourth can be found. Thus, in the work which you have been doing you have always known the principal, the rate per cent, and the time, and you have found the interest. PXRXT = I. To find the principal which will yield a certain amount of interest at a certain rate per cent in a given time, we divide the given interest by the interest on $1.00 for the given time at the given rate per cent, and as the interest on $1.00 for the given time at the given rate equals TR, therefore, I ÷ (T × R) = P. Exercise 64 Oral. 1. The interest for 60 days at 6% is what per cent of the principal? 2. If we know the interest for 60 days at 6%, how can we find the principal? Show this by letters and signs. 3. If we know the interest for 90 days at 6%, how can we find the principal? Show this by letters and signs. 4. If we know the interest for 60 days at 5%, how can we find the principal? Show this by letters and signs. 5. If we know the interest for 120 days at 5%, how can we find the principal? Show this by letters and signs. 6. What per cent of the principal is the amount due at the maturity of a 60-day 6% note? 7. If the correct answer to Question 6 is 101%, and you know the amount due at maturity, how do you find the principal in such an example? 8. How do you find the principal of a 30-day 5% note, if the amount due at maturity is known? Show this by letters and signs. 9. What four elements are involved in every interest example? 10. How many of these elements must be known, and how many may be unknown in any example? Exercise 65-Written. Solve, and prove by finding the interest: (Total interest interest on $1.= number of dollars ÷ in principal; I ÷ (T × R) What principal will yield: = P). 1. $12.00 in 180 days at 6%? Solve, and prove by finding the amount: (Total amount amount of $1. = number of dollars in principal; A ÷ (T × R + $1.00) = P). · What principal will amount to: 6. $406.00 in 4 months at 41%? LESSON 30. Finding the Time When the Principal, Rate, and Interest Are Given EXAMPLE: In what time will $420.00 yield $1.75 at 5%? The interest for 1 year at 5% on $420.00 = $21.00; 2100, or 12 year or 1 month, Ans. 1 X or 3 year or 1 month, Ans. I ÷ (P > R) $420. X, or $21.; I 1 year or 1 month, Ans. == To find the time in which a certain principal will yield a certain amount of interest at a certain rate per cent, we divide the total interest by 1 year's interest on the given principal at the given rate per cent, and as 1 year's interest on the given principal at the given rate per cent equals P × R, therefore, I ÷ (P × R) = T. EXAMPLE: In what time will $500.00 amount to $525.00 at 6%? $525.00 Interest on $500.00 for 1 yr. at 6% = $30.00; 500.00 Amount = Principal = Total = 25.00 $25.00 $30.00 Interest = year or 10 mo., Ans. When the amount due at maturity is given, subtract the principal from the amount to find the total interest, then continue as before. A P = I. Exercise 66-Written. Solve, and prove by finding the interest: (Total interest interest for 1 year = number of years in time; I ÷ (PX R) T). In what time will: = 1. $880.00 yield $10.45 at 43%? 2. $448.00 yield $36.96 at 51%? 3. $960.00 yield $45.60 at 63%? 4. $810.00 yield $31.50 at 5%? 5. $416.50 yield $83.30 at 6%? Solve, and prove by finding the amount: 6. $72.00 amount to $86.82 at 61%? 8. $876.00 amount to $883.30 at 5%? 9. $84.00 amount to $89.67 at 41%? 10. $1,080.00 amount to $1,143.00 at 7%? LESSON 31 Finding the Rate Per Cent When the Principal, EXAMPLE: At what rate per cent will $450.00 yield $11.25 P XT = $450. × 1, or $225.; I = $11.25; $11.25 ÷ $225. .05 or 5%, Ans. = To find the rate per cent at which a certain principal will yield a certain interest in a certain time, we divide the total interest by the interest at 1% on the given principal for the given time, and as the interest at 1% on the given principal for the given time is equal to 10 of (P x T), therefore, if we divide I by (P × T) the answer will be in hundredths instead of per cents. EXAMPLE: At what rate per cent will $816.00 amount to $907.80 in 2 years? = $907.80 The interest on $816.00 at 1% for 2 816.00 years equals $20.40; 91.80 $91.80 ÷ $20.40 = 2-180, or 41%, Ans. When the amount due at maturity is given, subtract the principal from the amount to find the total interest, and continue as before. A − P = I. |