Questions: 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 17,000 deposit in an account with an APR of 4.5%. The balance in the account after 1 year is approximately . (Round to the nearest cent as needed.)

The balance after 1 years is $17782.47, and the Annual Percentage Yield (APY) is 4.6%.

To convert the APR of 4.5% to a decimal, we divide by 100: \(r = 4.5 / 100 = 0.045\).

Using the formula \(A = Pe^{rt}\), where \(P = 17000\), \(r = 0.045\), and \(t = 5\), we find: \(A = 17000e^{0.045 \times 5} = 21289.49\).

Using the formula \( ext{APY} = (e^r - 1) \times 100%\), where \(r = 0.045\), we find: \( ext{APY} = (e^{0.045} - 1) \times 100% = 4.6%\).

The balance after 5 years is $21289.49, and the Annual Percentage Yield (APY) is 4.6%.

To convert the APR of 4.5% to a decimal, we divide by 100: \(r = 4.5 / 100 = 0.045\).

Using the formula \(A = Pe^{rt}\), where \(P = 17000\), \(r = 0.045\), and \(t = 20\), we find: \(A = 17000e^{0.045 \times 20} = 41813.25\).

Using the formula \( ext{APY} = (e^r - 1) \times 100%\), where \(r = 0.045\), we find: \( ext{APY} = (e^{0.045} - 1) \times 100% = 4.6%\).