SOLUTION: Cate purchases $1600 worth of stock and her broker estimates it will increase in value by 4.2% each year. after about how many years will the value of Cate's stock be about $2000?

Question 1085341: Cate purchases $1600 worth of stock and her broker estimates it will increase in value by 4.2% each year. after about how many years will the value of Cate's stock be about $2000?

Found 2 solutions by jorel1380, addingup:
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Since the money appreciates 4.2% each year, then:
2000=1600x(1.042)^n, where n is the number of years
Then:
1.25=1.042^n
ln 1.25=ln 1.042^n=n ln 1.042
n=5.424 years
🙂🙂🙂🙂

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
1600(1+0.042)^t = 2000
(1+0.042)^t = 2000/1600 = 5/4
log((1.042)^t) = log(5/4)
the log of a number raised to a power is equal to the power times the log of the number:
t*log(1.042) = log(5/4
t = log(5/4)/log(1.042)
change of base: log(a)/log(b) = log_b(a)
t = log_1.042(5/4) = 5.42 years
-----------------------------
check:
1600(1+0.042)^5.42 = 2000 correct

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