Question

Sam invests $ 4500 into an account earning 7.25% interest compounded quarterly. How long will it take to double his money?

Doubling time in years =

Answer 1

Hmm not sure wish I could help

Answer 2

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{doubled}{\$9000}\\ P=\textit{original amount deposited}\dotfill &\$4500\\ r=rate\to 7.25\%\to (7.25)/(100)\dotfill &0.0725\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases}`

`9000=4500\left(1+(0.0725)/(4)\right)^(4\cdot t) \implies \cfrac{9000}{4500}=\left(1+(0.0725)/(4)\right)^(4\cdot t) \\\\\\ 2=1.018125^(4t)\implies \log(2)=\log(1.018125^(4t))\implies \log(2)=t\log(1.018125^(4)) \\\\\\ \cfrac{\log(2)}{\log(1.018125^(4))}=t\implies 9.65\approx t\qquad \textit{about 9 years and 8 months}`