Question

I need help number 2 question b and c

Answer 1

To determine the value of a continous compound investment:

(b) Write a function that determine the value of the investment:

$\begin{gathered} f(t)=f_oe^{rt} \\ P\mleft(t\mright)=valueattimetP_0=originalprincipalsumr=nominalannualinterestratet=lengthoftimetheinterestisapplied \end{gathered}$$\begin{gathered} F(t)=f_0e^{rt} \\ f_0=2100 \\ r=3.4\text{ \%=0.034} \\ F(t)=2100e^{0.034t} \\ wheret=\text{ number of years } \end{gathered}$

(c) Annual Percentage Yield APY for continous compounding

$\begin{gathered} APY=e^r-1 \\ APY=e^{0.034}-1 \\ \text{APY}=1.03458-1 \\ \text{APY}=0.03458 \\ \text{APY}=3.458\text{ \%} \end{gathered}$