Answer: 28.0 years
Step-by-step explanation:
The formula we use to find the compounded amount after t years by putting a rate r on Principal value P is :
[tex]A=P(1+r)^x[/tex]
As per given , we have
P=$3200 , r=5.25%=0.0525 , A= $13400
Put all values in formula , we get
[tex]13400=3200(1+0.0525)^x\\\\\Rightarrow\ (1.0525)^x=\dfrac{13400}{3200}=4.1875\\\\\Rightarrow\ (1.0525)^x=4.1875[/tex]
Taking log on both sides , we get
[tex]x\log(1.0525)=\log(4.1875)\\\\\Rightarrow x(0.0222221045077)=0.621954820045\\\\\Rightarrow\ x=\dfrac{0.621954820045}{0.0222221045077}=27.9881151594\approx28.0[/tex]
Hence, it will take 28.0 years .
