(Solved): 2. Use the compound interest formula to find the total amount if $1 is invested at 100% interest for ...

2. Use the compound interest formula to find the total amount if $\$1$ is invested at $100\%$ interest for 1 year, when the number of compounding per year, $n$, is as follows: a) $n=1$ b) $n=10$ c) $n=100$ Notice that as $\mathrm{n}$ grows larger, the total gets closer and closer to $e$ dollars. 3. The variables in the compound interest formula are: $A,P,n,r$ and $t$. One of these variables will be missing in the continuously compounded interest formula. Which one, and why? 4. The continuously compounded interest formula is $A=P{e}^{rt}$. Use it to find the total if a) $\$100$ is invested at $6\%$ interest, compounded continuously, for one year. b) $\$4500$ is invested for 7 years at $5\%$ interest, compounded continuously. c) $\$1$ is invested for 1 year at $100\%$ interest, compounded continuously.