Answer:
Step-by-step explanation:
This is a problem about compound interest, which formula is:
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]
[tex]F[/tex]: Future value. ($200,000)
[tex]P[/tex]: Present value. ($3,000)
[tex]r[/tex]: Annual percentage rate (APR) changed into a decimal. (7%)
[tex]t[/tex]: Numbers of years. (?)
[tex]n[/tex]: Number of compounding periods per year (12)
Replacing all given values into the formula, we have:
[tex]200,000=3,000(1+\frac{0.07}{12})^{12t}[/tex]
[tex]200,000=3,000(1+\frac{0.07}{12})^{12t}\\\frac{200,000}{3,000}=(1.006)^{12t}\\66.67=(1.006)^{12t}\\ln66.67=ln((1.006)^{12t})\\ln66.67=12t(ln(1.006))\\t=\frac{ln66.67}{12(ln(1.006))}\\t \approx 58.5[/tex]
Therefore, approximately 58 months to grow the account to $200,000.
