SOLUTION: The amount of money in an account with continuously compounded interest is given by the formula {{{A=Pe^rt}}}, where P is the principal, r is the annual interest rate, and t is the

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The amount of money in an account with continuously compounded interest is given by the formula {{{A=Pe^rt}}}, where P is the principal, r is the annual interest rate, and t is the      Log On


   

Question 252472: The amount of money in an account with continuously compounded interest is given by the formula A=Pe%5Ert, where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 5.5%. Round to the nearest tenth.
Found 2 solutions by drk, stanbon:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We want our money to double. P = principal, A = 2*principal = 2P. r = 5.5% or 0.055. So, we have
A+=+Pe%5Ert
2P+=+Pe%5E0.055%2At
canceling the P and taking a natural log "LN" of both sides, we get
ln%282%29+=+.055t
solving for t, we get
t ~ 12.60 years to the nearest hundredth of a year.
t ~ 12 years 220 days to the nearest tenth.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 5.5%. Round to the nearest tenth.
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A(t) = Pe^(rt)
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If you invest "P", doubling will give you "2P".
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2P = Pe^(0.055t)
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2 = e^(0.055t)
Take the natural log of both sides to solve for "t":
0.055t = ln(2)
t = 12.6 years
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Cheers,
Stan H.