Question

how long will it take for $2700 to grow to $24500 at an interest rate of 2.2% if the interest is compounded quarterly? Round to the nearest hundredth.

Answer 1

Let n be the number of quarterlies.

Then

`\begin{gathered} 24500=2700(1+0.022)^n \\ \Rightarrow1.022^n=(245)/(27) \\ \Rightarrow n=(\log _(10)(245)/(27))/(\log _(10)1.022) \end{gathered}`

Hence the number of months = 3n = 304.04 months

and the number of years = n / 4 = 25.34 years