Given
Deposit = $4,000
APR of 3.7%.
continuous compounding
Find
The balance in the account after 1 year is approximately $
Explanation
given , deposit = $4000
APR = 3.7%
amount after 1 year
future value =
[tex]\begin{gathered} 4000\times e^{0.037\times1} \\ 1.0376930208382\times4000 \\ 4150.77208335\approx4150.77 \\ \end{gathered}[/tex]amount after 5 years
[tex]\begin{gathered} 4000\times e^{0.037\times5} \\ 1.2032184401277\times4000 \\ 4812.87376051\approx4812.87 \\ \end{gathered}[/tex]amount after 20 years
[tex]\begin{gathered} 4000\times e^{0.037\times20} \\ 2.0959355144944\times4000 \\ 8383.74205798\approx8383.74 \\ \end{gathered}[/tex]APY for the account =
[tex]e^{0.037}-1=1.0376930208382-1=0.0376930208382=3.77\%[/tex]Final Answer
Hence , the balance in the account after 1 year is approximately $4150.77
APY for the account is 3.77%
