March 8 Compound Interest
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March 8 Compound Interest

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March 8 Compound Interest March 8 Compound Interest Presentation Transcript

  • Compound Interest
  • Example Calculate the interest and the final amount if $1000 is borrowed for 1 year at 8%.
  • I = prt p (r) (t) I A 1000 (.08) (1) 80 1080
  • 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?
  • p (r) (t) I A 1000 (.08) (1) 80 $1080 1080 (.08) (1) 86.40 $1166.40
  • What if he still didn't pay it back for another year?
  • 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
  • What about another year?
  • 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
  • Another?
  • 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
  • This is called compound interest. The interest builds on itself. You pay interest on the interest.
  • 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
  • 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
  • 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
  • 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