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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

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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.)

Jan 14, 2015

#1
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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.

Jan 14, 2015

#1
+17774
+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