If Tanisha has $1,000 to invest at 6% per annum compounded semiannually, how long will it be before she has $1,350? If the compounding is continuous how long will it be

Answer:The Time period for investment at 6 % semiannually is 27 yearsStep-by-step explanation:Given as :The principal investment = $ 1000The rate of interest = 6% compounded semiannuallyThe Amount after T year = $ 1350Let the time period = T yearNow, From compounded method Amount = Principal × [tex](1+\dfrac{\textrm Rate}{6\times 100})^{\textrm time\times 6}[/tex]or, $ 1350 = $1000 × [tex](1+\dfrac{\textrm 6}{6\times 100})^{\textrm T\times 6}[/tex]Or, [tex]\frac{1350}{1000}[/tex] = [tex](1.01)^{T}[/tex]Or, 1.35 =  [tex](1.01)^{T}[/tex]or, [tex](1.31)^{\frac{1}{T}}[/tex] = 1.01 Now Taking log both sideLog  [tex](1.31)^{\frac{1}{T}}[/tex = Log 1.01Or, [tex]\frac{1}{T}[/tex] × 0.11727 = 0.0043213So, T = [tex]\frac{0.11727}{0.0043213}[/tex]∴ T = 27.11 ≈ 27 yearsHence The Time period for investment at 6 % semiannually is 27 years . Answer