Emilio invests $1,000 at 7.5% compounded quarterly. How long, to the nearest month will take for the investment to grow to $1,500?

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Answer 1 · 2017-05-26T11:40:43

#$1000# will take #5# years #6# months to grow to #$1500#

Let it be #n# years. Given : #P=1000 , F=1500 , r= 7.5%#(quarterly)

# :. r/400= 0.01875 # . Formula #F=P* (1+r/400)^(4*n) #

# :.1500 = 1000(1+.01875)^(4n) or (1.01875)^(4n)= 1500/1000 # or

# (1.01875)^(4n)= 1.5 #. Taking log on both sides we get,

#4nlog(1.01875) = log (1.5) or 4n = log (1.5)/log(1.01875) # or

#4n= 21.8269:. n =5.4567# year.

#:. n=5.4567# years or #5# years #5# months #14# days

#$1000# will take #5# years #6# months to grow to #$1500# [Ans]