March 8 Compound Interest

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March 8 Compound Interest

  1. 1. Compound Interest
  2. 2. Example Calculate the interest and the final amount if $1000 is borrowed for 1 year at 8%.
  3. 3. I = prt p (r) (t) I A 1000 (.08) (1) 80 1080
  4. 4. What if the person did not pay back the loan? What would be the new amount owing if he didn't pay it back for another year?
  5. 5. p (r) (t) I A 1000 (.08) (1) 80 $1080 1080 (.08) (1) 86.40 $1166.40
  6. 6. What if he still didn't pay it back for another year?
  7. 7. p (r) (t) I A 1000 (.08) (1) 80 $1080 1080 (.08) (1) 86.40 $1166.40 1166.40 (.08) (1) 93.31 $1259.71
  8. 8. What about another year?
  9. 9. p (r) (t) I A 1000 (.08) (1) 80 $1080 1080 (.08) (1) 86.40 $1166.40 1166.40 (.08) (1) 93.31 $1259.71 1259.71 (.08) (1) 100.78 $1360.49
  10. 10. Another?
  11. 11. p (r) (t) I A 1000 (.08) (1) 80 $1080 1080 (.08) (1) 86.40 $1166.40 1166.40 (.08) (1) 93.31 $1259.71 1259.71 (.08) (1) 100.78 $1360.49 1360.46 (.08) (1) 108.84 $1469.32
  12. 12. This is called compound interest. The interest builds on itself. You pay interest on the interest.
  13. 13. There is a formula to answer the example more quickly. A = p (1 + r/n) nt A = the final amount (principal plus interest) p = the principal r = rate in decimal form n = the number of times interest will be paid in a year t = time in years
  14. 14. Example A = p (1 + r/n) nt p = 1000 r = .08 t =5 n=1 (1)(5) A = 1000(1 + .08/1) A = $1469.32
  15. 15. example 2 How much is owed if $1000 is borrowed for 2 year at 6% compounded semi- annually. p = 1000 r = .06 t=2 n=2 A = 1000(1 + .06/2) 2(2) A = $1125.51
  16. 16. Daily = once a day = 365 times per year Weekly = once a week = 52 times per year Monthly = once a month = 12 times per year Annually = once a year = 1 times per year Semi-annually = every 6 months = 2 times per year Quarterly = every 3 months = 4 times per year

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