Question

Pat deposits $6,000 into an account earning 4% compounded monthly. How long will it take the account to grow to $10,000?

Answer 1

You need to solve the following equation to find the value of t = required number of months:
\[\large 10000=6000(1+\frac{0.04}{12})^{t}\]

Answer 2

T=-538.42

Answer 3

To solve the equation, first divide both sides by 6000, giving
\[\large 1.6667=(1+\frac{0.04}{12})^{t}\]
Next we simplify the term in brackets and take logs of both sides:
\[\large \log 1.6667=t \log 1.0033\]
Now we divide both sides by log 1.0033 to give
\[\large t=\frac{\log 1.6667}{\log 1.0033}=you\ can\ calculate\]