Question 198153: How long, to the nearest tenth of a year, will it take $3500 to grow to $8000 at 6.5% annual interest compounded semiannually? How long, compounded continuously?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How long, to the nearest tenth of a year, will it take $3500 to grow to $8000 at 6.5% annual interest compounded semiannually?
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A(t) = P(1+(r/n))^(nt)
8000 = 3500(1+(0.065/2))^(2t)
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2.2857 = (1+(0.0325)^(2t)
Take the log to get:
(2t)log(1.0325) = log(2.2857)
2t = 25.8472
t = 12.9236 years
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How long, compounded continuously?
A(t) = Pe^(rt)
8000 = 3500e^(0.065t)
2.2857 = e^(0.065t)
Take the natural log to get
0.065t = ln(2.2857)
t = 12.718 years
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Cheers,
Stan H.
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