Question

How many years will it take for $197,000 to grow to be $554,000 if it is invested in an account with a quoted annual interest rate of 8% with monthly compounding of interest?

Answer 1

Answer:

12.97 years

Explanation:

$AV=PV(1+\frac{i}{n})^{nt}$

we have

$554000=197000(1+\frac{.08}{12})^{12t}$

solve for t

$2.812=1.006667^{12t}$

Recall that

$y=z^x\\log_zy=x$

which means that

$log_{(1.0067)}2.812=12t\\155.61=12t$

therefore the answer is about 12.97 years which you may or may not want to round to 13