If $20,000 is invested and compounded continuously for four years, at what rate would you need to compound to guarantee a final value of $100,000?

Question

The formula the prof said to use is
R/r (e^rn-1) R= amount invested r= interest rate n= years

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Answer 1 · 2018-07-21T11:14:29

Investment of #$20000# at #40.24%# rate will earn more than #$100000# in #4# years.

Formula for continuously compounded amount,

#A=P*e^(r/100*t) ;A,P,r,t # are the final amount , principle, rate of

interest, number of years for investment.

#A=$100000,P=$20000 , t=4, r = ? #

#:.A=P*e^(r/100*t) or 100000=20000* e^((4r)/100)# or

# e^((r)/25)= 100000/20000 or e^(r/25)=5# Taking natural

log on both sides we get, # (r/25) ln e = ln 5 ; [ln e=1] #

#:. (r/25) ~~ 1.6094 :. r = 25 *1.6094 ~~ 40.24 % #

Investment of #$20000# at #40.24%# rate will earn more than

#$100000# in #4# years. [Ans]