Question

suppose you deposit $25,000 in to a fund for which the annual interest rate is 5.3% compounded continuously. find the number of years it will take to double in value (round your answer to the nearest tenth of a year)

Answer 1

so, the principal is 25,000, when it double then, the accumulated amount is 50,000.


`\bf \qquad \textit{Continuously Compounding Interest Earned Amount}\\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\to &\$50000\\ P=\textit{original amount deposited}\to& \$25000\\ r=rate\to 5.3\%\to (5.3)/(100)\to &0.053\\ t=years \end{cases} \\\\\\ 50000=25000e^(0.053t)\implies \cfrac{50000}{25000}=e^(0.053t)\implies 2=e^(0.053t) \\\\\\ ln(2)=ln(e^(0.053t))\implies ln(2)=0.053t\implies \cfrac{ln(2)}{0.053}=t \\\\\\ 13.0782486898102888\approx t\implies 13.08\approx t`