Final answer:
To compute the balance in the account after 1, 5, and 20 years, use the formula for continuous compounding: A = P*e^(rt). For a $400 deposit with an APR of 2.8%, the balances are $410.10 after 1 year, $454.90 after 5 years, and $647.01 after 20 years. The APY for the account is 2.83%.
Step-by-step explanation:
To compute the balance in the account after 1, 5, and 20 years using continuous compounding, we can use the formula: A = P×e^(rt). Where:
- A is the final balance
- P is the initial deposit
- e is Euler's number (approximately 2.71828)
- r is the annual interest rate in decimal form
- t is the number of years
For the given deposit of $400 and an APR of 2.8%, we can calculate the balance after 1 year:
A = 400 × e^(0.028×1) = $410.10
Similarly, for 5 years:
A = 400 × e^(0.028×5) = $454.90
And for 20 years:
A = 400 × e^(0.028×20) = $647.01
To find the APY (Annual Percentage Yield), we can use the formula: APY = (e^r - 1) × 100.
For the given APR of 2.8%, the APY is: APY = (e^0.028 - 1) × 100 = 2.83%