Question

Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account.A $4,000 deposit in an account with an APR of 3.7%.Question content area bottomThe balance in the account after 1 year is approximately $  (Round to the nearest cent as needed.)

Answer 1

Given

Deposit = $4,000

APR of ​3.7%.

continuous compounding

Find

The balance in the account after 1 year is approximately ​$

Step-by-step explanation

given , deposit = $4000

APR = 3.7%

amount after 1 year

future value =

`\begin{gathered} 4000* e^(0.037*1) \\ 1.0376930208382*4000 \\ 4150.77208335\approx4150.77 \\ \end{gathered}`

amount after 5 years

`\begin{gathered} 4000* e^(0.037*5) \\ 1.2032184401277*4000 \\ 4812.87376051\approx4812.87 \\ \end{gathered}`

amount after 20 years

`\begin{gathered} 4000* e^(0.037*20) \\ 2.0959355144944*4000 \\ 8383.74205798\approx8383.74 \\ \end{gathered}`

APY for the account =

`e^(0.037)-1=1.0376930208382-1=0.0376930208382=3.77\%`

Final Answer

Hence , the balance in the account after 1 year is approximately ​$4150.77

APY for the account is 3.77%