Answer:
The Time period for investment at 6 % semiannually is 27 years
Step-by-step explanation:
Given as :
The principal investment = $ 1000
The rate of interest = 6% compounded semiannually
The Amount after T year = $ 1350
Let the time period = T year
Now, 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 side
Log [tex](1.31)^{\frac{1}{T}}[/tex = Log 1.01
Or, [tex]\frac{1}{T}[/tex] × 0.11727 = 0.0043213
So, T = [tex]\frac{0.11727}{0.0043213}[/tex]
∴ T = 27.11 ≈ 27 years
Hence The Time period for investment at 6 % semiannually is 27 years . Answer
