Chapter 10 Examples, 1 Chapter 10 End-of-Chapter Problems: Examples Below are some worked-out examples for problems at the end of Chapter 10. Remember, you will want to do as many as it takes to feel comfortable with the material, and always feel free to post questions in the discussion area. Chapter 10 Formulas Simple Interest (I) = Principle (P) x Rate (R) x Time (T) Maturity Value (MV) = Principal (P) + Interest (I) Reminders! 1. Remember that percent is representative only, and must be converted to a decimal or a fraction prior to being used as a multiplier or divider! 2. The rates (R) used to determine interest are based on years, so the time (T) must always be converted to its equivalent in years. Drill Problems: 10-1: Given: Principal (P): $7,800 Rate (P): 4 and 1/4% = .0425 Time (T): 18 months = 18/12 = 1-1/2 years I=PxRxT I = $7,800 x .0425 x 18/12 I = $497.25 MV = $7,800 + $497.25 = $8,297.25 10-2: Given: Principal (P): $4,500 Rate (R): 3% = .03 Time (T): 6 months = 6/12 years I=PxRxT I = $4,500 x .03 x 6/12 I = $67.50 MV = $4,500 + $67.50 MV = $4,567.50 Chapter 10 Examples, 2 10-4: Using ordinary interest method (1 year = 360 days). You will need Table 7.1 to work problems 10-4 through 10-13. Given: P = $1,000 R = 8% = .08 Date borrowed: March 8 Date repaid: June 9 From Table 7.1: March 8 = day #67 June 9 = Day #160 Exact Time = 160 - 67 = 93 days I = ($1,000) x (.08) x (93 days/360 days) I = $20.67 MV = $1,000 + $20.67 = $1,020.67 10-8: Using exact interest method (365 days per year) Given: P = $585 R = 9% = .09 Date borrowed: June 5 Date repaid: December 15 From Table 7.1: June 5 = Day # 156 December 15 = Day # 349 Exact Time = 349 - 156 = 193 days I = ($585) x (.09) x (193 days/365 days) = $27.84 I = $27.84 MV = $585 + $27.84 = $612.84 10-12: Solve for Rate (R): R = I (P x T) Given: P = $5,000 T = 6 months I = $300 R = ($300) ($5,000 x 6/12), convert T fraction (6/12) to a decimal, .5 years R = ($300) ($5,000 x .5) R = $300/$2,500 R = .12 = 12% Chapter 10 Examples, 3 Try some of the drill problems, and post any questions to the discussion forum for Chapter 10 questions! Word Problems: Note: Remember that percent is representative only, and must be converted to a decimal prior to being used as a multiplier or divider! 10-14: Diane Van Os decided to buy a used snowmobile. She borrowed $2,700 at 3.5% on December 26, 2014, and paid it off on February 21, 2016. How much did she pay in interest (Assume ordinary interest.) Given: Principal (P): $2,700 Rate (R): 3.5% = .035 Time (T): 365 - 360 = 5 days left in 2012 + 365 days (2013) + 52 days in 2014 Time (T) = 422 days I = $2,700 x .035 x 422/360 I = $110.78 Answer: Diane paid $110.78 in interest. 10-16: Jody Jansen and Sunshine Bank Given Principal (P): $2,300 Rate (R): 9% = .09 Date Borrowed: September 12 Date Due: January 27th Ordinary Interest (360 days/year) Solve for: Interest (I) and Maturity Value (MV) First, we need to know how many days there are in the loan period. Back to Table 7.1! September 12 = Day #255 January 27 = Day #27 To determine the time period, subtract September day from 365 to get the days left in the year: 360 - 255 = 110 days, then add the number of days in January: 110 + 27 = 137 days Now that we know the total number of days, we can calculate the interest that will be owing on January 27th. So, back to the Simple Interest Formula: I=PxRxT Chapter 10 Examples, 4 I = ($2,300) x (.09) x (137 days/360 days) I = $78.78, now, solve for the Maturity Value (MV) MV = $2,300 + $78.78 = $2,378.78 Answer: Jody will owe $78.78 in interest on January 27th, as part of a Maturity Value of $2,378.78 10-17: Kelly O'Brien and Jody Jansen Kelly recommends to Jody (problem 10-16) that she ask the bank to calculate interest using the exact method (365 days/year): I = ($2,300) x (.09) x (137 days/365 days) I = $77.70, therefore the Maturity Value will be: MV = $2,300 + $77.70 = $2,377.70 Answer: Jody's Interest and Maturity Value would be $77.70 and $2,377.70 respectively if calculated using the exact method. The savings for using exact interest is $1.08. 10-30: Shawn Bixby borrowed $17,000 on a 120-day, 12% note. After 65 days, Shawn paid $2,000 on the note. On day 89, Shawn paid an additional $4,000. What is the final balance due? Determine total interest and ending balance due by the U.S. Rule. Use Ordinary interest. On Day 65: 65 days of Interest I = $17,000 x .12 x 65/360 I = $368.33 Partial Payment: $2,000 - $368.33 = $1,631.67 to Principal Adjusted Balance (AB) = $17,000 - $1,631.67 AB = $15,368.33 On Day 89: 24 days of Interest (89 - 65 = 24 days) I = $15,368.33 x .12 x 24/360 I = $122.95 Partial Payment: $4,000 - $122.95 = $3,877.05 to Principal Adjusted Balance (AB) = $15,368.33 - $3,877.05 AB = $11,491.28 At Maturity, 120 days: 31 days of Interest (120 - 89 = 31 days) I = $11,491.28 x .12 x 31/360 I = $118.74 Maturity Value (MV) = AB + Interest MV = $11,491.28 + $118.74 MV = $11,610.02 Total Interest = $368.33 + $122.95 + $118.74 Chapter 10 Examples, 5 Total Interest = $610.02 Answer: The ending balance is $11,610.02, with total interest of $610.02. 10-31: Carol Miller went to Europe and forgot to pay her $740 mortgage payment on her New Hampshire ski house. For her 59 days overdue on her payment, the bank charged her a penalty of $15. What was the rate of interest charged by the bank? Round to the nearest hundredth percent. (Assume ordinary interest) Given: Principal (P): $740 Interest (I): $15 Time (T): 59 days/360 days R = I/(P x T) R = $15/($740 x (59/360) R = $15/$121.28 R = .12368 x 100% R = 12.368% R = 12.37%, rounded to the nearest hundredth percent Answer: The bank's interest rate for the late payment is 12.37%. 10-32: Evander Holyfield made $250 million during his boxing career declared bankruptcy because of poor financial choices. His July interest at 15% was $155. What was Evander's principal at the beginning of August (assume 360 days)? Given: Interest (I): $155 Rate (R): 14% Time (T): 31/360 Principal (P) = I/(R x T) P = $155/(.15 x 31/360) P = $155/.012916 P = $12,000 Answer: Evander's principal at the beginning of August was $12,000. 10-33: Joey Logano won the 57th Daytona 500 in February 2015. If he paid back a $6,800 loan with $20 interest at 7.5%, what was the time of the loan (Assume 360 days)? Given: Principal (P): $6,800 Rate (R): 7.5% = .075 Interest (I) = $20 Chapter 10 Examples, 6 Time (T) = I/(P x R) T = $20/($6,800 x .075) T = $20/$510 T = .039215 years x 360 days/year = 14.12 days = 15 days Answer: The loan was outstanding for 15 days. Now try the word problems, and post your questions in the Discussion forum