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Question 795434: how long will it take $2000 to grow to $24000 is it is invested at 5% compounded monthly
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Use the formula
(1) B = P*(1 + r/12)^(12*t)
Where
B = balance of the investment of
P = principal amount after which appreciates at
r = annual rate for
t = years when compounded
monthly = 12
Then you have
(2) 24000 = 2000*(1+0.05/12)^(12*t) or
(3) 12 = (1 + 5/1200)^(12*t)
Take the ln of each side to get
(4) ln(12) = 12*t*ln(1 + 5/1200) or
(5) t = ln(12)/(12*ln(1+5/1200))
Using your scientific calculator (a necessity) to get
(6) t = 50.8+ years
Answer: It will take about 50.8 years for the $2000 investment to grow to $24,000, when the annual 5% rate is compounded monthly.
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