1. MDFP Mathematics and Statistics 1 COMPOUND Interest

2. MDFP – MAS 1 Money Lesson 19

3. Money – Loans and Investments – Today’s Class 1. Money – Loans and Investments 1. Compound Interest 2. EXAMPLES 3. Practice – Exercise 1 - 2 from Workbook 2. Conclusion Money – Loans and Investments3

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5. Compound Interest Formula Regarding the variables, n refers to the number of compoundings in any one year, not to the total number of compoundings over the life of the investment. If interest is compounded  yearly, then n = 1;  semi-annually, then n = 2;  quarterly, then n = 4;  monthly, then n = 12;  weekly, then n = 52;  daily, then n = 365; and so forth, regardless of the number of years involved. Money – Loans and Investments5

6. Compound Interest Formula Also, "t " must be expressed in years, because interest rates are expressed that way.  If an exercise states that the principal was invested for six months, you would need to convert this to 6 / 12 = 0.5 years;  if it was invested for 15 months, then t = 15 / 12 = 1.25 years;  if it was invested for 90 days, then t = 90 / 365 of a year = 0.25 years; and so on. Money – Loans and Investments6

7. Compound Interest Formula - Example Looks complicated? Let’s simplify the equation! For instance, let the interest rate r be 3%, compounded monthly, and let the initial investment amount be $1250. Then the compound-interest equation, for an investment period of t years, becomes: A c =1250(1 + 0.03/12 ) 12t = 1250(1.0025) 12t Money – Loans and Investments7

8. Compound Interest Formula - Example A c =1250(1 + 0.03/12 ) 12t = 1250(1.0025) 12t...where the base is 1.0025 and the exponent is the linear expression 12t.  To do compound-interest word problems, generally the only hard part is figuring out which values go where in the compound-interest formula.  Once you have all the values plugged in properly, you can solve for whichever variable is left. Money – Loans and Investments8

9. Example 1 Suppose that you plan to need $10,000 in thirty-six months' time when you start university. You want to invest in an instrument yielding 3.5% interest, compounded monthly. How much should you invest? To solve this, I have to figure out which values go with which variables! Money – Loans and Investments9

10. Example 1 In this case, you want to end up with $10,000, so A = 10,000. The interest rate is 3.5%, so, expressed as a decimal, r = 0.035. You have thirty-six months, so t = 36 / 12 = 3 years And the interest is compounded monthly, so n = 12. The only remaining variable is P, which stands for how much you started with. Money – Loans and Investments10

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14. Money – Loans and Investments Example 1 Now I'll do the whole simplification in my calculator, working from the inside out, so everything is carried in memory and I get as exact an answer as possible: Solution:I need to invest about $9004.62. Money – Loans and Investments14

15. Money – Simple and Compound Interest - Practice Practice on Exercise 1 – 2 from Workbook Money – Loans and Investments15

16. Money – Loans and Investments - Conclusion What did you learn today? Why do you need to learn about Loans and Investments ? Assignment: Any work not completed during class must be completed for homework Money – Loans and Investments16