Answer:
18 years (to the nearest year)
Step-by-step explanation:
Compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where A is amount, P is principal, r is interest rate (decimal format), n is the number of times interest is compounded per unit 't', and t is time
Given:
[tex]\implies 4490=2400(1+\frac{0.035}{12})^{12t}[/tex]
[tex]\implies \dfrac{449}{240}=\left(\dfrac{2407}{2400}\right)^{12t}[/tex]
[tex]\implies \ln\dfrac{449}{240}=\ln\left(\dfrac{2407}{2400}\right)^{12t}[/tex]
[tex]\implies \ln\dfrac{449}{240}=12t\ln\left(\dfrac{2407}{2400}\right)[/tex]
[tex]\implies t=\dfrac{\ln\dfrac{449}{240}}{12\ln\left(\dfrac{2407}{2400}\right)}[/tex]
[tex]\implies t=17.92277136...[/tex]
Therefore, it would take 18 years (to the nearest year) for the account to reach $4,490
