A deposit of $2000 is invested in an account that earns 4.5% interest. The duration of time before the balance reaches $3000 is 9.2 years.
From the given information;
- the principal deposited amount = 2000
- the annual interest rate = 4.5%
- the amount (A) estimated in t years = 3000
The time required until your balance reaches the amount of 3000 can be estimated by using the given formula;
[tex]\mathbf{A = P ( 1+ r)^t}[/tex]
[tex]\mathbf{3000 = 2000 ( 1+ \dfrac{4.5}{100})^t}[/tex]
[tex]\mathbf{3000 = 2000 ( 1+ 0.045)^t}[/tex]
[tex]\mathbf{3000 = 2000 ( 1.045)^t}[/tex]
[tex]\mathbf{3 = 2( 1.045)^t}[/tex]
[tex]\mathbf{( 1.045)^t= \dfrac{3}{2}}[/tex]
[tex]\mathbf{( 1.045)^t= 1.5}[/tex]
[tex]\mathbf{( 1.045)^t= 1.5}[/tex]
t = 9.2 years
Therefore, we can conclude that the time duration (in years) until your balance reaches $3000 is 9.2.
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