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Aim # 14: How Do We Determine the Income from our Investments?

Aim # 14: How Do We Determine the Income from our Investments?. CD Rate is 1.2%. Do Now. Julie Fee is a real estate broker who earns 8.5% commission on each house she sells. If she earned $35,700 on a house she sold, what was the selling price of the house?. Answer: $420,000. Minilesson :.

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Aim # 14: How Do We Determine the Income from our Investments?

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  1. Aim # 14: How Do We Determine the Income from our Investments? CD Rate is 1.2%

  2. Do Now Julie Fee is a real estate broker who earns 8.5% commission on each house she sells. If she earned $35,700 on a house she sold, what was the selling price of the house? Answer: $420,000

  3. Minilesson: Formula for Interest Earned on a Deposit: This is I = prt Where I = simple interest earned p = your original deposit r = interest rate as a decimal t = period of time (in our case, 1 yr)

  4. Minilesson (cont’d): For any question, Either follow the wording of the verbal problem, Set-up a table (to help organize your thoughts) OR YOU decide

  5. Minilesson (cont’d): Either follow the wording of the verbal problem, = Interest Rate for Investment Amount Earned Amount Invested X

  6. Minilesson (cont’d): Either follow the wording of the verbal problem, Total Amount Earned from BOTH Investments Amt Earned Investment # 1 Amt Earned Investment # 2 = +

  7. Minilesson (cont’d): Set-up a table (to help organize your thoughts) X = Interest Rate Amt Earned Amt Invested

  8. Minilesson (cont’d): Set-up a table (to help organize your thoughts) X = Interest Rate Amt Earned Amt Invested Investment # 1 Investment # 2

  9. Guided Practice Handout, qq. 318 – 319, qq. 1, 2, 7

  10. Independent Practice Handout Aim # 14, qq. 5, 6, 8, 9, 10

  11. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.035 m 0.035m Investment # 2 0.08 9000 —m 0.08(9000 —m) Note: First investment income exceeds 2nd by $ 16.

  12. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.035 m 0.035m Investment # 2 0.08 9000 —m 0.08(9000 —m) Note: 1st minus 2nd equals 16

  13. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.035 m 0.035m Investment # 2 0.08 9000 —m 0.08(9000 —m)

  14. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.035 m 0.035m Investment # 2 0.08 9000 —m 0.08(9000 —m) Multiply through by 1000.

  15. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.035 m 0.035m Investment # 2 0.08 9000 —m 0.08(9000 —m) Distribute 80 across parentheses.

  16. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.035 m 0.035m Investment # 2 0.08 9000 —m 0.08(9000 —m) NOTICE: Minus sign changed to plus.

  17. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8% X = Interest Rate Amt Earned Amt Invested Investment # 1 0.035 m 0.035m Investment # 2 0.08 9000 —m 0.08(9000 —m) Combine like terms.

  18. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.035 m 0.035m Investment # 2 0.08 9000 —m 0.08(9000 —m)

  19. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.035 m 0.035m Investment # 2 0.08 9000 —m 0.08(9000 —m) Divide both sides by coefficient 115.

  20. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % ANSWER $6,400 invested at 3.5% $2,600 invested at 8%

  21. Independent Practice (cont’d) Let m = amt invested at 3.5 % Question 5 9000 — m = amt invested at 8 % $6,400 invested at 3.5% $2,600 invested at 8% CHECK 0.035(6400) = 224 0.08(2600) = 208 It works!! 224 − 208 = 16 

  22. Independent Practice (cont’d) The remaining is $9000 minus the sum of the first two investments Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — (m+2m) = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 Investment # 2

  23. Independent Practice (cont’d) The remaining is $9000 minus the sum of the first two investments Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 Investment # 2

  24. Independent Practice (cont’d) The remaining is $9000 minus the sum of the first two investments Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.06 m 0.06m 0.045(2m) 0.045 2m Investment # 2 Investment # 3 0.02 0.02(9000 —3m) 9000 —3m Note: The money earned on the three investments is $360.

  25. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.06 m 0.06m 0.045(2m) 0.045 2m Investment # 2 Investment # 3 0.02 0.02(9000 —3m) 9000 —3m Note: 1st plus 2nd plus 3rd equals 360

  26. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.06 m 0.06m 0.045(2m) 0.045 2m Investment # 2 Investment # 3 0.02 0.02(9000 —3m) 9000 —3m

  27. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.06 m 0.06m 0.045(2m) 0.045 2m Investment # 2 Investment # 3 0.02 0.02(9000 —3m) 9000 —3m 000

  28. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.06 m 0.06m 0.045(2m) 0.045 2m Investment # 2 Investment # 3 0.02 0.02(9000 —3m) 9000 —3m 000

  29. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.06 m 0.06m 0.045(2m) 0.045 2m Investment # 2 Investment # 3 0.02 0.02(9000 —3m) 9000 —3m Combine like terms. 000

  30. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.06 m 0.06m 0.045(2m) 0.045 2m Investment # 2 Investment # 3 0.02 0.02(9000 —3m) 9000 —3m Combine like terms. 000 The 60m cancels out.

  31. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.06 m 0.06m 0.045(2m) 0.045 2m Investment # 2 Investment # 3 0.02 0.02(9000 —3m) 9000 —3m Subtract from both sides. 000

  32. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.06 m 0.06m 0.045(2m) 0.045 2m Investment # 2 Investment # 3 0.02 0.02(9000 —3m) 9000 —3m Divide both sides. 000

  33. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % ANSWER $2,000 invested at 6% $4,000 invested at 4.5% $3,000 invested at 2%

  34. Independent Practice (cont’d) Let m = amt invested at 6 % Question 6 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % CHECK! 0.06(2,000) + 0.045(4000) + 0.02(3000) + 180 + 60 360 

  35. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.03 m 0.03m Investment # 2 0.05 8000 —m 0.05(8000 —m) Note: Man LOST money from 2nd Investment.

  36. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.03 m 0.03m Investment # 2 0.05 8000 —m 0.05(8000 —m) Note: GAIN of 1st + LOSS 2nd = Net Income.

  37. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.03 m 0.03m Investment # 2 —0.05(8000 —m) 0.05 8000 —m Note: GAIN of 1st + LOSS 2nd= Net Income.

  38. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.03 m 0.03m Investment # 2 —0.05(8000 —m) 0.05 8000 —m

  39. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.03 m 0.03m Investment # 2 —0.05(8000 —m) 0.05 8000 —m

  40. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.03 m 0.03m Investment # 2 —0.05(8000 —m) 0.05 8000 —m Distributive Property changes signs.

  41. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.03 m 0.03m Investment # 2 —0.05(8000 —m) 0.05 8000 —m

  42. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.03 m 0.03m Investment # 2 —0.05(8000 —m) 0.05 8000 —m

  43. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.03 m 0.03m Investment # 2 —0.05(8000 —m) 0.05 8000 —m

  44. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % ANSWER $6,000 invested at 3% $2,000 invested at 5%

  45. Independent Practice (cont’d) Let m = amt invested at 3 % Question 8 8000 — m = amt invested at 5 % CHECK 0.03(6,000) = $180 MINUS 0.05(2,000) = $100 Net Gain = $ 80 

  46. Independent Practice (cont’d) Let m = amt invested at 5 % Question 9 9600 — m = amt invested at 3.5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.05 m 0.05m Investment # 2 0.035 9600 —m 0.035(9600 —m) Note: 1st Investment yields twice 2nd Investment.

  47. Independent Practice (cont’d) Let m = amt invested at 5 % Question 9 9600 — m = amt invested at 3.5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.05 m 0.05m Investment # 2 0.035 9600 —m 0.035(9600 —m) Twice the amt earned from 2nd investment

  48. Independent Practice (cont’d) Let m = amt invested at 5 % Question 9 9600 — m = amt invested at 3.5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.05 m 0.05m Investment # 2 0.035 9600 —m 0.035(9600 —m) Doubled 0.035 Doubled 0.35

  49. Independent Practice (cont’d) Let m = amt invested at 5 % Question 9 9600 — m = amt invested at 3.5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.05 m 0.05m Investment # 2 0.035 9600 —m 0.035(9600 —m) Multiply through by 100

  50. Independent Practice (cont’d) Let m = amt invested at 5 % Question 9 9600 — m = amt invested at 3.5 % X = Interest Rate Amt Earned Amt Invested Investment # 1 0.05 m 0.05m Investment # 2 0.035 9600 —m 0.035(9600 —m) Distribute the 7.

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