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

Question

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

amistre64 · Answer

1006.64 = 500(1+.06/4)^(4*t)

amistre64 · Answer

1006.64
------- = [1+(.06/4)]^(4t)
    500

amistre64 · Answer

log(2.01328) = log(1.015)^4t


log(2.01328)
----------- = 4t
  log(1.015)


log(2.01328)
------------ = t
  4 log(1.015)

amistre64 · Answer

t = 11.75 years

t = 11 yrs and 9 mths

amistre64 · Answer

dble check by using this value of t in the original

amistre64 · Answer

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 · Answer

1006.6395513857092257218559330282 when you dont truncate it lol