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Simple & Compound Interest

Simple & Compound Interest. Simple Interest. -Interest paid only on an initial amount deposited or the amount borrowed. -The amount is called the PRINCIPLE. Term. -The length of TIME in years over which the $$ is deposited or borrowed. Often expressed as “PER ANNUM”.

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Simple & Compound Interest

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  1. Simple & CompoundInterest

  2. Simple Interest -Interest paid only on an initial amount deposited or the amount borrowed -The amount is called the PRINCIPLE

  3. Term -The length of TIME in years over which the $$is deposited or borrowed Often expressed as “PER ANNUM”

  4. The amount of simple interest accumulated on an investment or loan is calculated using this formula Calculating Formula

  5. I = the amount of interest earned or due I = Prt P = the Principle r = the annual interest rate (expressed as a decimal) t = the term of investment or loan

  6. For an investment: Calculate the total value at the end of the term using this formula:

  7. A = P + I A=final value of the investment P=Principle I=Amount of Interest

  8. You want to invest $5000 in an account that offers simple interest. Example How much would the investment be worth at the end of a 2yr term at 3%?

  9. First change the interest rate to a decimle 3% = .03 Principle = $5000 Term = 2yrs

  10. I = $5000 x .03 x 2ys I = Prt I= $300 Now calculate the final value A=P+I A= $5000 + $300 A=$5300

  11. Converting Interest to a decimal 4.75% converted to a decimal =4.75 ÷ 100 = .0475

  12. Use the same Principleand calculate at a rate of 3.75% for 4 yrs I = $5000 x .0375 x 4 = $750 Calculate the final value A = $5000 + $750 = $5750

  13. Let’s Try Shall we?

  14. Compound Interest

  15. A type of interest that is calculated on the principle, plus any interest PREVIOUSLY earned

  16. -If you invest $$ for two years, but earn interest annually… Example -the second year of interest will be calculated on the initial principle PLUS the interest it earned in the 1st year

  17. -$5000 @ 3% for 2 yrs calculated using COMPOUND Interest Example Year 1 I = $5000 x .03 x 1yr = $150 A = $5000 + $150 = $5150

  18. Year 2 I = $5150 x .03 x 1 = $154.50 A = $5150 + $154.50 = $5304.50 Example Therefore - $5000 compounded “annually” over 2yrs @ 3% = a return of $304.50

  19. If the interest is compounded annually = once/yr Compounding Period Investments can have different compounding periods

  20. Interest can be calculated “SEMI-Annually” Twice/year Example Interest can be calculated “QUARTERLY” 4 x per year

  21. Interest can be calculated “MONTHLY” Once/Month Example Interest can be calculated “DAILY”

  22. A = P(1+r ) n nt Calculation Formula A = Final Value P = Principle r = Interest Rate n = Number of compound periods t = term of investment/loan

  23. Example Calculate the interest earned on $1000 put in an account that offers 4%/annum compounded annually for 2yrs

  24. nt • A = P(1+r ) • n Example 1x2 A = $1000 x (1 + 0.04 ) 1 A = $1000 x (1.04) 2 A = $1081.60

  25. I = $1000 x 4% x 2 Compare w/Simple Interest I = $1000 x .04% x 2 I = $80 A = $1000 + $80 = $1080 Compound Int. = $1081.60

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