What equation models the growth of William and Monica's account balance over time in years if they deposit $20,000 into an account that pays 4.75% interest, compounded daily?

A. [tex]A = 20000 \times \left(1 + \frac{0.0475}{365}\right)^{365t}[/tex]
B. [tex]A = 20000 \times \left(1 + \frac{0.0475}{365}\right)^8[/tex]
C. [tex]A = 20000 \times (1 + 0.0475)^8[/tex]
D. [tex]A = 20000 \times \left(1 + \frac{0.0475}{365}\right)^{365 \times 8}[/tex]

What would be the account balance after 8 years if no additional deposits or withdrawals are made?

The correct compound interest equation for the account balance, compounded daily, is A = 20000 × (1 + 0.0475/365)365t. To find the balance after 8 years, plug in the values to get the future value. The correct option is a.

Explanation:

The equation that models the growth of William and Monica's account balance over time, with interest being compounded daily, is given by A = 20000 × (1 + 0.0475/365)365t.

This is the standard formula for compound interest where 'A' is the account balance after 't' years, the initial deposit is $20,000, the annual interest rate is 4.75%, and the number of times the interest is compounded per year is 365.

To calculate the account balance after 8 years with no additional deposits or withdrawals, we just need to plug in the values into the formula: A = 20000 × (1 + 0.0475/365)365×8

After performing this calculation, we find out the account balance that William and Monica will have after the 8-year period. The correct option is a.