Question

Rich also has £400 pounds invest 3% compound interest . How many years does he need to invest the money to get at least £475

Answer 1

Answer: 6 years

Step-by-step explanation:

Formula to calculate compound amount: $A=P(1+r)^t$, where P= Principal , r=rate of interest, t= time

Given: P = £400, r = 3% = 0.03 , A= 475

Required equation: $400(1+0.03)^t\geq475$

$400(1.03)^t\geq475\\\\\Rightarrow\ (1.03)^t\geq\dfrac{475}{400}\\\\\Rightarrow\ (1.03)^t\geq1.1875$

Taking log on both sides , we get

$t \log 1.03\geq\log1.1875\\\\\Rightarrow\ t(0.0128372)\geq(0.0746336)\\\\\Rightarrow\ t\geq\dfrac{0.0746336}{0.0128372}=5.81385\approx6$

Hence, he needs to invest the money for 6 years to get atleast £475.