anonymous
  • anonymous
How many years will it take for a $500 to grow to $1006.64 at 6% interest compounded quarterly? A) 11.50 years B) 11.75 years C) 12.00 years D) 12.25 years E) 12.50 years
Mathematics
jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
1006.64 = 500(1+.06/4)^(4*t)
amistre64
  • amistre64
1006.64 ------- = [1+(.06/4)]^(4t) 500
amistre64
  • amistre64
log(2.01328) = log(1.015)^4t log(2.01328) ----------- = 4t log(1.015) log(2.01328) ------------ = t 4 log(1.015)

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amistre64
  • amistre64
t = 11.75 years t = 11 yrs and 9 mths
amistre64
  • amistre64
dble check by using this value of t in the original
amistre64
  • amistre64
1006.64=500(1.015)^(4*11.75) 1006.54 = 500(1.015)^47 1006.54 = 500(2.01) 1006.54 = 1005 ...because i chopped the decimal off to much lol
amistre64
  • amistre64
1006.6395513857092257218559330282 when you dont truncate it lol

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