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Account a and b each start with $400. If account a earn $45 each year and account b earns 5% of its value each year when will account b have more money than account a

Respuesta :

Answer:  [tex]T>2.185[/tex] year

Step-by-step explanation:

[tex]A=P\left ( 1+R/100\right )^{T}[/tex]

[tex]A=Amount ,P=Principle , R=Rate , T=Time[/tex]

CI=compound interest

[tex]CI=A-P[/tex]

[tex]P=400\$[/tex]  for each a and b

account earn each year by a=[tex]45\$[/tex]

account b earns  [tex]5%[/tex]%

find the time the value of b is more

[tex]45<400\left ( 1+5/100 \right )^{T}-400[/tex]

[tex]445<\left 400\left ( 1+5/100 \right )^{T}[/tex]

[tex]445/400<\left ( 21/20 \right )^{T}[/tex]

[tex]\ln \left ( 445/400 \right )<T\ln \left ( 21/20 \right )[/tex]

[tex].106609735<.0487901642\times T[/tex]

[tex]=2.1850<T[/tex]

[tex]T>2.185[/tex] year

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