Answer: 6 years
Step-by-step explanation:
Formula to calculate compound amount: [tex]A=P(1+r)^t[/tex], where P= Principal , r=rate of interest, t= time
Given: P = £400, r = 3% = 0.03 , A= 475
Required equation: [tex]400(1+0.03)^t\geq475[/tex]
[tex]400(1.03)^t\geq475\\\\\Rightarrow\ (1.03)^t\geq\dfrac{475}{400}\\\\\Rightarrow\ (1.03)^t\geq1.1875[/tex]
Taking log on both sides , we get
[tex]t \log 1.03\geq\log1.1875\\\\\Rightarrow\ t(0.0128372)\geq(0.0746336)\\\\\Rightarrow\ t\geq\dfrac{0.0746336}{0.0128372}=5.81385\approx6[/tex]
Hence, he needs to invest the money for 6 years to get atleast £475.
