I. 1. Find the interest of $450 for 120 days at 8%. SOLUTION BY FORMULA: I. Since I = P x R × T, .'. I II. EXAMPLES 1. Since 100% of principal = $450, 66 66 2. ... 1% 3. and 8% 66 1. Since int. for 360 days II. 2. ... int. for 1 day 3. and int. for 120 days 120 × $0.1 NOTE.-In ordinary business transactions, 30 days are considered a month, and 360 days a year. SOLUTION BY ANALYSIS: Substituting: R 66 = $450 180 × 128 = = = Using the formula above, make a formula for finding the principal, the rate, and the time. Write the rule for each formula made. = = 2. At what rate will $360 produce $24 interest in 1 year and 4 months? SOLUTION: Since I = P × R × T, ... R = $24 $360 × 13 Too of $450 = $4.50. 8 × $4.50 $36, = int. for 1 yr. $36, 360 of $36 = $0.1, $12. = = = ANALYSIS: 12. 1. Since int. for 1 yr. 4 mo., or 3 yr., .. the rate = 5%. = = = I P× T .05, or 5%. $12. = $24, of 100% % of the principal, %, or 5% of the principal. I. 3. In what time will $480 produce $60 at 5%? II. I $60 Px R' $480 × .05 NOTE. The solution by the formula is purely mechanical. It will do for commercial purposes, but for educational purposes the solution by analysis is far more valuable. ANALYSIS: I. II. Since T III. 2. .... 3. and = 1. Since 100% of prin. 66 66 1% .. SOLUTION: T = 1. Since $24 is the int. for 1 yr., 66 66 66 66 2. .. $1 3. and $60 1. Since 100% of prin. 2. 66 1% " = = = 4. What principal will amount to $2394 in 2 years and 4 months at 6%? = SOLUTION: Assume $1 as a principal. $1, Too of $1 = $480, Too of $480 = = 24 yr., "60 × 24 yr., or 21 yr. = 3. and 6% $0.06, 1. Since the int. for 1 yr. 1. Since $1.14 am't requires $1 prin., 66 "" 2. ... $1 $r prin., 3. and $2394 2394 $ prin.=$2100 prin. SHORT PROCESS: = = 21, or 21 yr. $4.80, $24. = 6 × $0.01 = $0.01, $0.06. = 1. Int. on $1 for 2 yr. 4 mo. at 6% NOTE.-By means of the solution above, the present worth of a debt is found. 341. The present worth of a debt payable at a future date without interest is that sum which, when put on interest for the time yet to elapse, will amount to the debt. The above example might be stated thus: What is the present worth of $2394, due 2 yr. 4 mo. hence, money being worth 6%, simple interest? 342. The true discount is the difference between the debt and the present worth. It is, therefore, the simple interest on the present worth. 5. Find the present worth and true discount of a debt of $627 due in 9 months, money being worth 6%. SOLUTION: The meaning is: $600 put on interest at 6% for 9 mo. would amount to $627. Solve this problem by analysis, following the form in example 4 above. NOTE.-In true discount, it is not customary to allow 3 days of grace. 343. In bankers' interest (bank discount), the exact number of days is counted; but, in expressing the time in years, 360 days is considered 1 year. Thus, the time from May 2, 1904, to August 5, 1904, is 95 days, or 3 95 yr. 344. In exact interest, the exact number of days is counted; but, in expressing the time in years, 365 days is considered 1 year (366 days in leap years). Thus, the time from January 1, 1904, to July 12, 1904, is 193 days, or 1 yr. Exercise XL Find the simple interest on: 1. $370 for 2 years at 5%. 3. $1342 for 8 months at 10%. 4. $1 for 30 days at 6%. 5. $1 for 1 day at 1%. Find the amount of: 6. $1568 for 5 yr. 8 mo. 18 da. at 8%. Find the rate required for: 8. $400 to produce $57 int. in 1 yr. 7 mo. 9. $900 to produce $25.20 int. in 8 mo. 12 da. Find the time required for: 10. $500 to produce $55 interest at 8%. 11. $2500 to produce $131.25 interest at 7%. Find the principal which amounts to: 14. $751.20 in 6 mo. 15 da. at 8%. 15. $2516.663 in 30 da. at 8%. 16. $240.50 from Sept. 1 to Dec. 31, at 4%. Find the interest (bankers' interest method) on: 17. $385 from Aug. 12, 1891. to Nov. 1, 1891, at 12%. 18. $840 from May 12, 1904, to Sept. 5, 1904, at 8%. |