Question

Nathan is going to invest in an account paying an interest rate of 4. 9% compounded continuously. How much would Nathan need to invest, , for the value of the account to reach $34,000 in 9 years?

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$34000\\ P=\textit{original amount deposited}\\ r=rate\to 4.9\%\to (4.9)/(100)\dotfill &0.049\\ t=years\dotfill &9 \end{cases} \\\\\\ 34000=Pe^(0.049\cdot 9)\implies 34000=Pe^(0.441)\implies \cfrac{34000}{e^(0.441)}=P\implies 21875.35\approx P`