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.)
+23246 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)n
---> 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.
+23246 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)n
---> 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.
