You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $200,000?

It would take around 67 monthes

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Answer:

58 months

Step-by-step explanation:

This is a problem about compound interest, which formula is:

$F=P(1+\frac{r}{n})^{nt}$

$F$ : Future value. ($200,000)

$P$ : Present value. ($3,000)

$r$ : Annual percentage rate (APR) changed into a decimal. (7%)

$t$ : Numbers of years. (?)

$n$ : Number of compounding periods per year (12)

Replacing all given values into the formula, we have:

$200,000=3,000(1+\frac{0.07}{12})^{12t}$

$200,000=3,000(1+\frac{0.07}{12})^{12t}\\\frac{200,000}{3,000}=(1.006)^{12t}\\66.67=(1.006)^{12t}\\ln66.67=ln((1.006)^{12t})\\ln66.67=12t(ln(1.006))\\t=\frac{ln66.67}{12(ln(1.006))}\\t \approx 58.5$

Therefore, approximately 58 months to grow the account to $200,000.

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