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Use logarithms to solve the problem. How long will it take an investment of $2000 to triple if the investment earns interest at the rate of 3%/year compounded daily? (Round your answer to two decimal places.)

Guest Jan 14, 2015

Best Answer 

 #1
avatar+17721 
+5

Compound Interest Formula:     A  =  P(1 + r/n)^(n·t)

A = final amount = $6000.00         P = beginning amont = $2000.00         t = time (in years)

r = rate (as a decimal) = 0.03        n = number of compounding periods per year = 1

--->   6000  =  2000(1 + 0.03/1)^(n·1)

--->   6000  =  2000(1.03)n

--->   3  =  (1.03)

--->   log(3)  =  log(1.03)n             Now, since exponents come out as multipliers:

--->  log(3)  =  n·log(1.03)             Divide both sides by log(1.03):

--->  log(3) / log(1.03)  =  n          Use a calculator to make this division, and round your answer.

geno3141  Jan 14, 2015
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1+0 Answers

 #1
avatar+17721 
+5
Best Answer

Compound Interest Formula:     A  =  P(1 + r/n)^(n·t)

A = final amount = $6000.00         P = beginning amont = $2000.00         t = time (in years)

r = rate (as a decimal) = 0.03        n = number of compounding periods per year = 1

--->   6000  =  2000(1 + 0.03/1)^(n·1)

--->   6000  =  2000(1.03)n

--->   3  =  (1.03)

--->   log(3)  =  log(1.03)n             Now, since exponents come out as multipliers:

--->  log(3)  =  n·log(1.03)             Divide both sides by log(1.03):

--->  log(3) / log(1.03)  =  n          Use a calculator to make this division, and round your answer.

geno3141  Jan 14, 2015

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