The time taken for her to reach the amount of $106,200 will be 17 years.
What is compound interest?
Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-
Given that:-
- Alexa invested $54,000 in an account paying an interest rate of 4% compounded continuously.
The formula for calculating the compound interest continuously.
[tex]A \ = \ P e^ {rt}[/tex]
[tex]106200\ = \ 54000e^{0.04t}\\\\\\\dfrac{106200}{54000}=e^{0.04t}\\\\\\1.97\ = \ e^{0.04t}\\\\\\Ln(1.97)=Ln(e^{0.04t})[/tex]
Ln(1.97) = 0.04t
t = 17 years.
Therefore the time taken for her to reach the amount of $106,200 will be 17 years.
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