How many years will it take $2,000 invested at 6% to earn $360?

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Answer 1 · 2017-12-23T09:17:31

3 years

In one year, yo can earn $120.
Just multiply $120 by 6% to get it.

Then divide $360 by $120.
The answer is 3.

Therefore, it will take 3 years to earn $360.

Answer 2 · 2017-12-23T09:24:17

Will take 3 years

Im guessing you mean there is an annual interest of #6%#

We can use the formula for compound interest...

#A = N_0 ( 1 + P/100 ) ^t #

#N_0 # - Initial amound

#P# - percentage

#t# - time in years

For us to earn #$360# it would mean to have #$2,360# in the account after #t# years

#=> 2360 = 2000*(1+6/100)^t #

Dividing by #2000# and simplifying...

#=> 59/50 = (53/50)^t #

Taking #log_10 # to both sides:

#=> log (59/50) = log (53/50)^t #

Using our log laws:

#logalpha^beta -= betalogalpha #

#=>log(59/50) = t*log(53/50) #

#=> t = log(59/50) / log(53/50) #

#=> t approx 2.841# years

#=> t = 3 # years